Foliations Dynamics Geometry And Topology

Author by : Masayuki Asaoka
Languange : en
Publisher by : Springer
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Description : This book is an introduction to several active research topics in Foliation Theory and its connections with other areas. It contains expository lectures showing the diversity of ideas and methods converging in the study of foliations. The lectures by Aziz El Kacimi Alaoui provide an introduction to Foliation Theory with emphasis on examples and transverse structures. Steven Hurder's lectures apply ideas from smooth dynamical systems to develop useful concepts in the study of foliations: limit sets and cycles for leaves, leafwise geodesic flow, transverse exponents, Pesin Theory and hyperbolic, parabolic and elliptic types of foliations. The lectures by Masayuki Asaoka compute the leafwise cohomology of foliations given by actions of Lie groups, and apply it to describe deformation of those actions. In his lectures, Ken Richardson studies the properties of transverse Dirac operators for Riemannian foliations and compact Lie group actions, and explains a recently proved index formula. Besides students and researchers of Foliation Theory, this book will be interesting for mathematicians interested in the applications to foliations of subjects like Topology of Manifolds, Differential Geometry, Dynamics, Cohomology or Global Analysis.


Foliations Geometry And Topology

Author by : Paul A. Schweitzer
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume represents the proceedings of the conference on Foliations, Geometry, and Topology, held August 6-10, 2007, in Rio de Janeiro, Brazil, in honor of the 70th birthday of Paul Schweitzer. The papers concentrate on the theory of foliations and related areas such as dynamical systems, group actions on low dimensional manifolds, and geometry of hypersurfaces. There are survey papers on classification of foliations and their dynamical properties, including codimension one foliations with Bott - Morse singularities. Other papers involve the relationship of foliations with characteristic classes, contact structures, and Eliashberg - Mishachev wrinkled mappings.


Geometry Dynamics And Topology Of Foliations A First Course

Author by : Bruno Scardua
Languange : en
Publisher by : World Scientific
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Description : The Geometric Theory of Foliations is one of the fields in Mathematics that gathers several distinct domains: Topology, Dynamical Systems, Differential Topology and Geometry, among others. Its great development has allowed a better comprehension of several phenomena of mathematical and physical nature. Our book contains material dating from the origins of the theory of foliations, from the original works of C Ehresmann and G Reeb, up till modern developments.In a suitable choice of topics we are able to cover material in a coherent way bringing the reader to the heart of recent results in the field. A number of theorems, nowadays considered to be classical, like the Reeb Stability Theorem, Haefliger's Theorem, and Novikov Compact leaf Theorem, are proved in the text. The stability theorem of Thurston and the compact leaf theorem of Plante are also thoroughly proved. Nevertheless, these notes are introductory and cover only a minor part of the basic aspects of the rich theory of foliations.


Singularities And Foliations Geometry Topology And Applications

Author by : Raimundo Nonato Araújo dos Santos
Languange : en
Publisher by : Springer
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Description : This proceedings book brings selected works from two conferences, the 2nd Brazil-Mexico Meeting on Singularity and the 3rd Northeastern Brazilian Meeting on Singularities, that were hold in Salvador, in July 2015. All contributions were carefully peer-reviewed and revised, and cover topics like Equisingularity, Topology and Geometry of Singularities, Topological Classification of Singularities of Mappings, and more. They were written by mathematicians from several countries, including Brazil, Spain, Mexico, Japan and the USA, on relevant topics on Theory of Singularity, such as studies on deformations, Milnor fibration, foliations, Catastrophe theory, and myriad applications. Open problems are also introduced, making this volume a must-read both for graduate students and active researchers in this field.


Laminations And Foliations In Dynamics Geometry And Topology

Author by : Mikhail Lyubich
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume is based on a conference held at SUNY, Stony Brook (NY). The concepts of laminations and foliations appear in a diverse number of fields, such as topology, geometry, analytic differential equations, holomorphic dynamics, and renormalization theory. Although these areas have developed deep relations, each has developed distinct research fields with little interaction among practitioners. The conference brought together the diverse points of view of researchers from different areas. This book includes surveys and research papers reflecting the broad spectrum of themes presented at the event. Of particular interest are the articles by F. Bonahon, ``Geodesic Laminations on Surfaces'', and D. Gabai, ``Three Lectures on Foliations and Laminations on 3-manifolds'', which are based on minicourses that took place during the conference.


Foliations Dynamics Geometry And Topology

Author by : Masayuki Asaoka
Languange : en
Publisher by : Birkhäuser
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Total Read : 15
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Description : This book is an introduction to several active research topics in Foliation Theory and its connections with other areas. It contains expository lectures showing the diversity of ideas and methods converging in the study of foliations. The lectures by Aziz El Kacimi Alaoui provide an introduction to Foliation Theory with emphasis on examples and transverse structures. Steven Hurder's lectures apply ideas from smooth dynamical systems to develop useful concepts in the study of foliations: limit sets and cycles for leaves, leafwise geodesic flow, transverse exponents, Pesin Theory and hyperbolic, parabolic and elliptic types of foliations. The lectures by Masayuki Asaoka compute the leafwise cohomology of foliations given by actions of Lie groups, and apply it to describe deformation of those actions. In his lectures, Ken Richardson studies the properties of transverse Dirac operators for Riemannian foliations and compact Lie group actions, and explains a recently proved index formula. Besides students and researchers of Foliation Theory, this book will be interesting for mathematicians interested in the applications to foliations of subjects like Topology of Manifolds, Differential Geometry, Dynamics, Cohomology or Global Analysis.


Foliations Geometry And Topology

Author by : Nicolau C. Saldanha
Languange : en
Publisher by : Unknown
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Description :


Foliations On Surfaces

Author by : Igor Nikolaev
Languange : en
Publisher by : Springer Science & Business Media
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Description : This book presents a comprehensive, encyclopedic approach to the subject of foliations, one of the major concepts of modern geometry and topology. It addresses graduate students and researchers and serves as a reference book for experts in the field.


Metric Diffusion Along Foliations

Author by : Szymon M. Walczak
Languange : en
Publisher by : Springer
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Description : Up-to-date research in metric diffusion along compact foliations is presented in this book. Beginning with fundamentals from the optimal transportation theory and the theory of foliations; this book moves on to cover Wasserstein distance, Kantorovich Duality Theorem, and the metrization of the weak topology by the Wasserstein distance. Metric diffusion is defined, the topology of the metric space is studied and the limits of diffused metrics along compact foliations are discussed. Essentials on foliations, holonomy, heat diffusion, and compact foliations are detailed and vital technical lemmas are proved to aide understanding. Graduate students and researchers in geometry, topology and dynamics of foliations and laminations will find this supplement useful as it presents facts about the metric diffusion along non-compact foliation and provides a full description of the limit for metrics diffused along foliation with at least one compact leaf on the two dimensions.


Geometry Of Foliations

Author by : Philippe Tondeur
Languange : en
Publisher by : Birkhäuser
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Description : The topics in this survey volume concern research done on the differential geom etry of foliations over the last few years. After a discussion of the basic concepts in the theory of foliations in the first four chapters, the subject is narrowed down to Riemannian foliations on closed manifolds beginning with Chapter 5. Following the discussion of the special case of flows in Chapter 6, Chapters 7 and 8 are de voted to Hodge theory for the transversal Laplacian and applications of the heat equation method to Riemannian foliations. Chapter 9 on Lie foliations is a prepa ration for the statement of Molino's Structure Theorem for Riemannian foliations in Chapter 10. Some aspects of the spectral theory for Riemannian foliations are discussed in Chapter 11. Connes' point of view of foliations as examples of non commutative spaces is briefly described in Chapter 12. Chapter 13 applies ideas of Riemannian foliation theory to an infinite-dimensional context. Aside from the list of references on Riemannian foliations (items on this list are referred to in the text by [ ]), we have included several appendices as follows. Appendix A is a list of books and surveys on particular aspects of foliations. Appendix B is a list of proceedings of conferences and symposia devoted partially or entirely to foliations. Appendix C is a bibliography on foliations, which attempts to be a reasonably complete list of papers and preprints on the subject of foliations up to 1995, and contains approximately 2500 titles.


Foliations Geometry And Dynamics

Author by : Paweł Walczak
Languange : en
Publisher by : World Scientific
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Description : This volume contains surveys and research articles regarding different aspects of the theory of foliation. The main aspects concern the topology of foliations of low-dimensional manifolds, the geometry of foliated Riemannian manifolds and the dynamical properties of foliations. Among the surveys are lecture notes devoted to the analysis of some operator algebras on foliated manifolds and the theory of confoliations (objects defined recently by W Thurston and Y Eliashberg, situated between foliations and contact structures). Among the research articles one can find a detailed proof of an unpublished theorem (due to Duminy) concerning ends of leaves in exceptional minimal sets. Contents:Survey Articles:Some Results on Secondary Characteristic Classes of Transversely Holomorphic Foliations (T Asuke)LS-Categories for Foliated Manifolds (H Colman)Dynamics and the Godbillon–Vey Class: A History and Survey (S Hurder)Similarity and Conformal Geometry of Foliations (R Langevin)Foliations and Contact Structures on 3-Manifolds (Y Mitsumatsu)Operator Algebras and the Index Theorem on Foliated Manifolds (H Moriyoshi)Research Articles:Distributional Betti Numbers of Transitive Foliations of Codimension One (J Álvarez-López & Y Kordyukov)Tautly Foliated 3-Manifolds with No R-Covered Foliations (M Brittenham)Endests of Exceptional Leaves — A Theorem of G Duminy (J Cantwell & L Conlon)Foliations and Compactly Generated Pseudogroups (A Haefliger)Transverse Lusternik–Schnirelmann Category and Non-Proper Leaves (R Langevin & P Walczak)On Exact Poisson Manifolds of Dimension 3 (T Mizutani)On the Perfectness of Groups of Diffeomorphisms of the Interval Tangent to the Identity at the Endpoints (T Tsuboi)and other papers Readership: Researchers interested in mathematics, especially in fields related to differential geometry and topology, and the theory of dynamical systems. Keywords:Proceedings;Workshop;Geometry;Warsaw (Poland);Dynamics;Euroworkshop


Singularities In Geometry Topology Foliations And Dynamics

Author by : José Luis Cisneros-Molina
Languange : en
Publisher by : Birkhäuser
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Description : This book features state-of-the-art research on singularities in geometry, topology, foliations and dynamics and provides an overview of the current state of singularity theory in these settings. Singularity theory is at the crossroad of various branches of mathematics and science in general. In recent years there have been remarkable developments, both in the theory itself and in its relations with other areas. The contributions in this volume originate from the “Workshop on Singularities in Geometry, Topology, Foliations and Dynamics”, held in Merida, Mexico, in December 2014, in celebration of José Seade’s 60th Birthday. It is intended for researchers and graduate students interested in singularity theory and its impact on other fields.


In The Tradition Of Thurston

Author by : Ken’ichi Ohshika
Languange : en
Publisher by : Springer Nature
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Description : This book consists of 16 surveys on Thurston's work and its later development. The authors are mathematicians who were strongly influenced by Thurston's publications and ideas. The subjects discussed include, among others, knot theory, the topology of 3-manifolds, circle packings, complex projective structures, hyperbolic geometry, Kleinian groups, foliations, mapping class groups, Teichmüller theory, anti-de Sitter geometry, and co-Minkowski geometry. The book is addressed to researchers and students who want to learn about Thurston’s wide-ranging mathematical ideas and their impact. At the same time, it is a tribute to Thurston, one of the greatest geometers of all time, whose work extended over many fields in mathematics and who had a unique way of perceiving forms and patterns, and of communicating and writing mathematics.


Confoliations

Author by : Y. Eliashberg
Languange : en
Publisher by : American Mathematical Soc.
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Description : This book presents the first steps of a theory of confoliations designed to link geometry and topology of three-dimensional contact structures with the geometry and topology of codimension-one foliations on three-dimensional manifolds. Developing almost independently, these theories at first glance belonged to two different worlds: The theory of foliations is part of topology and dynamical systems, while contact geometry is the odd-dimensional 'brother' of symplectic geometry. However, both theories have developed a number of striking similarities. Confoliations - which interpolate between contact structures and codimension-one foliations - should help us to understand better links between the two theories. These links provide tools for transporting results from one field to the other.It's features include: a unified approach to the topology of codimension-one foliations and contact geometry; insight on the geometric nature of integrability; and, new results, in particular on the perturbation of confoliations into contact structures.


Geometry And Topology

Author by : Martin A. Mccrory
Languange : en
Publisher by : CRC Press
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Description : This book discusses topics ranging from traditional areas of topology, such as knot theory and the topology of manifolds, to areas such as differential and algebraic geometry. It also discusses other topics such as three-manifolds, group actions, and algebraic varieties.


Extrinsic Geometry Of Foliations

Author by : Vladimir Rovenski
Languange : en
Publisher by : Springer Nature
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Description : This book is devoted to geometric problems of foliation theory, in particular those related to extrinsic geometry, modern branch of Riemannian Geometry. The concept of mixed curvature is central to the discussion, and a version of the deep problem of the Ricci curvature for the case of mixed curvature of foliations is examined. The book is divided into five chapters that deal with integral and variation formulas and curvature and dynamics of foliations. Different approaches and methods (local and global, regular and singular) in solving the problems are described using integral and variation formulas, extrinsic geometric flows, generalizations of the Ricci and scalar curvatures, pseudo-Riemannian and metric-affine geometries, and 'computable' Finsler metrics. The book presents the state of the art in geometric and analytical theory of foliations as a continuation of the authors' life-long work in extrinsic geometry. It is designed for newcomers to the field as well as experienced geometers working in Riemannian geometry, foliation theory, differential topology, and a wide range of researchers in differential equations and their applications. It may also be a useful supplement to postgraduate level work and can inspire new interesting topics to explore.


Analysis And Geometry In Foliated Manifolds Proceedings Of The 7th International Colloquium On Differential Geometry

Author by : Macias-virgos Enrique
Languange : en
Publisher by : World Scientific
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Description : Pesticides continue to provide an important tool in integrated pest management (IPM) programmes. Hitherto IPM programmes have had a strong bias towards insect control, but farmers need to control weeds, plant pathogens and other pest problems.This book follows the author's successful “pesticide application methods” by relating the equipment needs to the overall pest control requirement of major crops. It outlines the pest problems against which farmers are using pesticides and focusses on the details of the application techniques they need to optimise pesticide use.Much attention is now being given to genetically modified crops, but these do not necessarily avoid the use of pesticides. Some are engineered to be resistant to certain herbicides, so the use of these herbicides will still require careful application in order to minimise environmental side effects. Similarly, crops engineered for resistance to certain insect pest species may remain susceptible to other pests, thus emphasising the need for crop monitoring and careful use of any chemicals to avoid disrupting biological control.


Topology Of Foliations An Introduction

Author by : Ichirō Tamura
Languange : en
Publisher by : American Mathematical Soc.
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Description : This book provides historical background and a complete overview of the qualitative theory of foliations and differential dynamical systems. Senior mathematics majors and graduate students with background in multivariate calculus, algebraic and differential topology, differential geometry, and linear algebra will find this book an accessible introduction. Upon finishing the book, readers will be prepared to take up research in this area. Readers will appreciate the book for its highly visual presentation of examples in low dimensions. The author focuses particularly on foliations with compact leaves, covering all the important basic results. Specific topics covered include: dynamical systems on the torus and the three-sphere, local and global stability theorems for foliations, the existence of compact leaves on three-spheres, and foliated cobordisms on three-spheres. Also included is a short introduction to the theory of differentiable manifolds.


Geometry And Topology In Dynamics

Author by : Marcy Barge
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume consists of the written presentations of lectures given at two special sessions: the AMS Special Session on Topology in Dynamics (Winston-Salem, NC) and the AMS-AWM Special Session on Geometry in Dynamics (San Antonio, TX). Each article concerns aspects of the topology or geometry of dynamical systems. Topics covered include the following: foliations and laminations, iterated function systems, the three-body problem, isotopy stability, homoclinic tangles, fractal dimension, Morse homology, knotted orbits, inverse limits, contact structures, Grassmanians, blowups, and continua. New results are presented reflecting current trends in topological aspects of dynamical systems. The book offers a wide variety of topics of special interest to those working this area bridging topology and dynamical systems.


Geometric Theory Of Foliations

Author by : César Camacho
Languange : en
Publisher by : Springer Science & Business Media
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Description : Intuitively, a foliation corresponds to a decomposition of a manifold into a union of connected, disjoint submanifolds of the same dimension, called leaves, which pile up locally like pages of a book. The theory of foliations, as it is known, began with the work of C. Ehresmann and G. Reeb, in the 1940's; however, as Reeb has himself observed, already in the last century P. Painleve saw the necessity of creating a geometric theory (of foliations) in order to better understand the problems in the study of solutions of holomorphic differential equations in the complex field. The development of the theory of foliations was however provoked by the following question about the topology of manifolds proposed by H. Hopf in the 3 1930's: "Does there exist on the Euclidean sphere S a completely integrable vector field, that is, a field X such that X· curl X • 0?" By Frobenius' theorem, this question is equivalent to the following: "Does there exist on the 3 sphere S a two-dimensional foliation?" This question was answered affirmatively by Reeb in his thesis, where he 3 presents an example of a foliation of S with the following characteristics: There exists one compact leaf homeomorphic to the two-dimensional torus, while the other leaves are homeomorphic to two-dimensional planes which accu mulate asymptotically on the compact leaf. Further, the foliation is C"".


On The C Algebras Of Foliations In The Plane

Author by : Xiaolu Wang
Languange : en
Publisher by : Springer
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Description : The main result of this original research monograph is the classification of C*-algebras of ordinary foliations of the plane in terms of a class of -trees. It reveals a close connection between some most recent developments in modern analysis and low-dimensional topology. It introduces noncommutative CW-complexes (as the global fibred products of C*-algebras), among other things, which adds a new aspect to the fast-growing field of noncommutative topology and geometry. The reader is only required to know basic functional analysis. However, some knowledge of topology and dynamical systems will be helpful. The book addresses graduate students and experts in the area of analysis, dynamical systems and topology.


Three Dimensional Geometry And Topology

Author by : WILLIAM P AUTOR THURSTON
Languange : en
Publisher by : Princeton University Press
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Description : Every mathematician should be acquainted with the basic facts about the geometry of surfaces, of two-dimensional manifolds. The theory of three-dimensional manifolds is much more difficult and still only partly understood, although there is ample evidence that the theory of three-dimensional manifolds is one of the most beautiful in the whole of mathematics. This excellent introductory work makes this mathematical wonderland remained rather inaccessible to non-specialists. The author is both a leading researcher, with a formidable geometric intuition, and a gifted expositor. His vivid descriptions of what it might be like to live in this or that three-dimensional manifold bring the subject to life. Like Poincaré, he appeals to intuition, but his enthusiasm is infectious and should make many converts for this kind of mathematics. There are good pictures, plenty of exercises and problems, and the reader will find a selection of topics which are not found in the standard repertoire. This book contains a great deal of interesting mathematics.


Three Dimensional Geometry And Topology Volume 1

Author by : William P. Thurston
Languange : en
Publisher by : Princeton University Press
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Description : This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty. This book was the origin of a grand scheme developed by Thurston that is now coming to fruition. In the 1920s and 1930s the mathematics of two-dimensional spaces was formalized. It was Thurston's goal to do the same for three-dimensional spaces. To do this, he had to establish the strong connection of geometry to topology--the study of qualitative questions about geometrical structures. The author created a new set of concepts, and the expression "Thurston-type geometry" has become a commonplace. Three-Dimensional Geometry and Topology had its origins in the form of notes for a graduate course the author taught at Princeton University between 1978 and 1980. Thurston shared his notes, duplicating and sending them to whoever requested them. Eventually, the mailing list grew to more than one thousand names. The book is the culmination of two decades of research and has become the most important and influential text in the field. Its content also provided the methods needed to solve one of mathematics' oldest unsolved problems--the Poincaré Conjecture. In 2005 Thurston won the first AMS Book Prize, for Three-dimensional Geometry and Topology. The prize recognizes an outstanding research book that makes a seminal contribution to the research literature. Thurston received the Fields Medal, the mathematical equivalent of the Nobel Prize, in 1982 for the depth and originality of his contributions to mathematics. In 1979 he was awarded the Alan T. Waterman Award, which recognizes an outstanding young researcher in any field of science or engineering supported by the National Science Foundation.


Foliations 2012 Proceedings Of The International Conference

Author by : Jesus A Alvarez Lopez
Languange : en
Publisher by : World Scientific
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Description : This volume is a compilation of new results and surveys on the current state of some aspects of the foliation theory presented during the conference “FOLIATIONS 2012”. It contains recent materials on foliation theory which is related to differential geometry, the theory of dynamical systems and differential topology. Both the original research and survey articles found in here should inspire students and researchers interested in foliation theory and the related fields to plan his/her further research.


Extrinsic Geometry Of Foliations

Author by : Vladimir Rovenski
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 40
Total Download : 360
File Size : 54,8 Mb
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Description : This book is devoted to geometric problems of foliation theory, in particular those related to extrinsic geometry, modern branch of Riemannian Geometry. The concept of mixed curvature is central to the discussion, and a version of the deep problem of the Ricci curvature for the case of mixed curvature of foliations is examined. The book is divided into five chapters that deal with integral and variation formulas and curvature and dynamics of foliations. Different approaches and methods (local and global, regular and singular) in solving the problems are described using integral and variation formulas, extrinsic geometric flows, generalizations of the Ricci and scalar curvatures, pseudo-Riemannian and metric-affine geometries, and 'computable' Finsler metrics. The book presents the state of the art in geometric and analytical theory of foliations as a continuation of the authors' life-long work in extrinsic geometry. It is designed for newcomers to the field as well as experienced geometers working in Riemannian geometry, foliation theory, differential topology, and a wide range of researchers in differential equations and their applications. It may also be a useful supplement to postgraduate level work and can inspire new interesting topics to explore.


Differential Topology Foliations And Group Actions

Author by : Workshop on Topology
Languange : en
Publisher by : American Mathematical Soc.
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Total Read : 28
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Description : This volume contains the proceedings of the Workshop on Topology held at the Pontificia Universidade Catolica in Rio de Janeiro in January 1992. Bringing together about one hundred mathematicians from Brazil and around the world, the workshop covered a variety of topics in differential and algebraic topology, including group actions, foliations, low-dimensional topology, and connections to differential geometry. The main concentration was on foliation theory, but there was a lively exchange on other current topics in topology. The volume contains an excellent list of open problems in foliation research, prepared with the participation of some of the top world experts in this area. Also presented here are two surveys on group actions---finite group actions and rigidity theory for Anosov actions---as well as an elementary survey of Thurston's geometric topology in dimensions 2 and 3 that would be accessible to advanced undergraduates and graduate students.