Topics On Real And Complex Singularities

Author by : Alexandru Dimca
Languange : de
Publisher by : Vieweg+Teubner Verlag
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Description : The body of mathematics developed in the last forty years or so which can be put under the heading Singularity Theory is quite large. And the excellent introductions to this vast sub­ ject which are already available (for instance [AGVJ, [BGJ, [GiJ, [GGJ, [LmJ, [Mr], [WsJ or the more advanced [Ln]) cover necessarily only apart of even the most basic topics. The aim of the present book is to introduce the reader to a few important topics from ZoaaZ Singularity Theory. Some of these topics have already been treated in other introductory books (e.g. right and contact finite determinacy of function germs) while others have been considered only in papers (e.g. Mather's Lemma, classification of simple O-dimensional complete intersection singularities, singularities of hyperplane sections and of dual mappings of projective hypersurfaces). Even in the first case, we feel that our treatment is different from the introductions mentioned above - the general reason being that we give special attention to the aompZex anaZytia situation and to the connections with AZgebraia Geometry. We offer now a detailed description of the contents, pOint­ ing out special aspects and new material (i.e. previously un­ published, though for the most part surely known to the~ts!). Chapter 1 is a short introduction for the beginner. We recall here two basic results (the Submersion Theorem and Morse Lemma) and make a few comments on what is meant by the local behaviour of a function or of a plane algebraic curve.


Real And Complex Singularities

Author by : Jean-Paul Brasselet
Languange : en
Publisher by : Birkhäuser
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Description : This volume collects papers presented at the eighth São Carlos Workshop on Real and Complex Singularities, held at the IML, Marseille, July 2004. Like the workshop, this collection establishes the state of the art and presents new trends, new ideas and new results in all of the branches of singularities. Real and Complex Singularities offers a useful summary of leading ideas in singularity theory, and inspiration for future research.


Real And Complex Singularities

Author by : David Mond
Languange : en
Publisher by : CRC Press
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Description : This text offers a selection of papers on singularity theory presented at the Sixth Workshop on Real and Complex Singularities held at ICMC-USP, Brazil. It should help students and specialists to understand results that illustrate the connections between singularity theory and related fields. The authors discuss irreducible plane curve singularities, openness and multitransversality, the distribution Afs and the real asymptotic spectrum, deformations of boundary singularities and non-crystallographic coxeter groups, transversal Whitney topology and singularities of Haefliger foliations, the topology of hypersurface singularities, polar multiplicities and equisingularity of map germs from C3 to C4, and topological invariants of stable maps from a surface to the plane from a global viewpoint.


Real And Complex Singularities

Author by : Laurentiu Paunescu
Languange : en
Publisher by : World Scientific
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Description : The modern theory of singularities provides a unifying theme that runs through fields of mathematics as diverse as homological algebra and Hamiltonian systems. It is also an important point of reference in the development of a large part of contemporary algebra, geometry and analysis. Presented by internationally recognized experts, the collection of articles in this volume yields a significant cross-section of these developments. The wide range of surveys includes an authoritative treatment of the deformation theory of isolated complex singularities by prize-winning researcher K Miyajima. Graduate students and even ambitious undergraduates in mathematics will find many research ideas in this volume and non-experts in mathematics can have an overview of some classic and fundamental results in singularity theory. The explanations are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to go further into the subject and explore the research literature.


Real And Complex Singularities

Author by : James William Bruce
Languange : en
Publisher by : CRC Press
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Description : The boundaries of singularity theory are broad and vague, connecting the most important applications of mathematics and science with more abstract areas. Optics, robotics, computer vision, Hamiltonian mechanics, bifurcation theory and differential equations are among the variety of topics that benefit from developments in the theory. With singularity theory encompassing more and more applications, Real and Complex Singularities provides insight into the future of this expanding field. Comprising refereed contributions to the Fifth Workshop on Real and Complex Singularities, this volume addresses three important areas related to the broad subject of singularities. The first section deals with questions within singularity theory itself, representing the topics currently being investigated. The second explores applications of singularity theory to differential geometry, robotics, and computer vision. The final section consists of applications to bifurcation theory and dynamical systems. With over two-hundred tables that provide quick access to data, this volume is a complete overview of the most current topics and applications of singularity theory. Real and Complex Singularities creates the opportunity for you to stay up-to-date with recent advances and discover promising directions for future research in the field.


Real And Complex Singularities

Author by : W. L. Marar
Languange : en
Publisher by : CRC Press
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Description : Much progress has been made recently in a number of areas by the application of new geometrical methods arising from advances in singularity theory. This collection of invited papers presented at the 3rd International Workshop on Real and Complex Singularities, held in August 1994 at ICMSC-USP (Sao Carlos), documents the geometric study of singularities and its applications.


Topics On Real And Complex Singularities

Author by : Satoshi Koike
Languange : en
Publisher by : World Scientific
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Description : A phenomenon which appears in nature, or human behavior, can sometimes be explained by saying that a certain potential function is maximized, or minimized. For example, the Hamiltonian mechanics, soapy films, size of an atom, business management, etc. In mathematics, a point where a given function attains an extreme value is called a critical point, or a singular point. The purpose of singularity theory is to explore the properties of singular points of functions and mappings. This is a volume on the proceedings of the fourth Japanese–Australian Workshop on Real and Complex Singularities held in Kobe, Japan. It consists of 11 original articles on singularities. Readers will be introduced to some important new notions for characterizations of singularities and several interesting results are delivered. In addition, current approaches to classical topics and state-of-the-art effective computational methods of invariants of singularities are also presented. This volume will be useful not only to the singularity theory specialists but also to general mathematicians. Contents:On the CR Hamiltonian Flows and CR Yamabe Problem (T Akahori)An Example of the Reduction of a Single Ordinary Differential Equation to a System, and the Restricted Fuchsian Relation (K Ando)Fronts of Weighted Cones (T Fukui and M Hasegawa)Involutive Deformations of the Regular Part of a Normal Surface (A Harris and K Miyajima)Connected Components of Regular Fibers of Differentiable Maps (J T Hiratuka and O Saeki)The Reconstruction and Recognition Problems for Homogeneous Hypersurface Singularities (A V Isaev)Openings of Differentiable Map-Germs and Unfoldings (G Ishikawa)Non Concentration of Curvature near Singular Points of Two Variable Analytic Functions (S Koike, T-C Kuo and L Paunescu)Saito Free Divisors in Four Dimensional Affine Space and Reflection Groups of Rank Four (J Sekiguchi)Holonomic Systems of Differential Equations of Rank Two with Singularities along Saito Free Divisors of Simple Type (J Sekiguchi)Parametric Local Cohomology Classes and Tjurina Stratifications for μ-Constant Deformations of Quasi-Homogeneous Singularities (S Tajima) Readership: Mathematicians in singularity theory or in adjacent areas; advanced undergraduates and graduate students in mathematics; non-experts interested in singularity theory and its applications. Key Features:Contains applications of the singularity theory to other mathematical fieldsNew topics in singularity theory, e.g. the relationship between free divisors and holonomic systems, openings of differentiable map-germs, non-concentration of curvatureIncludes articles by prize-winning researchers like Kimio Miyajima and Osamu SaekiKeywords:Singularities;CR Structure;Deformation Theory;Free Divisor;Concentration of Curvature;Holonomic System;Front;Opening


Real And Complex Singularities

Author by : Jean-Paul Brasselet
Languange : en
Publisher by : Springer Science & Business Media
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Total Read : 77
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Description : This volume collects papers presented at the eighth São Carlos Workshop on Real and Complex Singularities, held at the IML, Marseille, July 2004. Like the workshop, this collection establishes the state of the art and presents new trends, new ideas and new results in all of the branches of singularities. Real and Complex Singularities offers a useful summary of leading ideas in singularity theory, and inspiration for future research.


Real And Complex Singularities

Author by : M. Manoel
Languange : en
Publisher by : Cambridge University Press
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Description : The biennial meetings at São Carlos have helped create a worldwide community of experts and young researchers working on singularity theory, with a special focus on applications to a wide variety of topics in both pure and applied mathematics. The tenth meeting, celebrating the 60th birthdays of Terence Gaffney and Maria Aparecida Soares Ruas, was a special occasion attracting the best known names in the area. This volume contains contributions by the attendees, including three articles written or co-authored by Gaffney himself, and survey articles on the existence of Milnor fibrations, global classifications and graphs, pairs of foliations on surfaces, and Gaffney's work on equisingularity.


Real And Complex Singularities

Author by : Marcelo José Saia
Languange : en
Publisher by : American Mathematical Soc.
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Description : This book offers a selection of papers based on talks presented at the Ninth International Workshop on Real and Complex Singularities, a series of biennial workshops organized by the Singularity Theory group at Sao Carlos, S.P., Brazil. The papers deal with all the different topics in singularity theory and its applications, from pure singularity theory related to commutative algebra and algebraic geometry to those topics associated with various aspects of geometry to homotopy theory. Among the topics on pure singularity theory discussed are invariants of singularities, integral closure and equisingularity, classification theory, contact structures and vector fields, and Thom polynomials. Geometric aspects deal with relations of singularity theory with topology, differential geometry and physics. Here topics discussed include the index of quadratic differential forms, obstructions in fundamental groups of plane curve complements, conjugate vectors of immersed manifolds, exotic moduli of Goursat distributions in codimension three, cobordisms of fold maps, etc. The book concludes with notes from the course on the residue theoretical approach to intersection theory.


Real And Complex Singularities

Author by : International Workshop on Real and Complex Singularities (7th 2002 Instituto de Cinci
Languange : en
Publisher by : American Mathematical Soc.
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Description : The Workshop on Real and Complex Singularities is held every other year at the Instituto de Ciencias Matematicas e de Computacao (Sao Carlos, Brazil) and brings together specialists in the vanguard of singularities and its applications. This volume contains articles contributed by participants of the seventh workshop.


Real And Complex Singularities

Author by : Victor Goryunov
Languange : en
Publisher by : American Mathematical Soc.
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Description : "This volume is a collection of papers presented at the 11th International Workshop on Real and Complex Singularities, held July 26-30, 2010, in Säao Carlos, Brazil, in honor of David Mond's 60th birthday. This volume reflects the high level of the conference discussing the most recent results and applications of singularity theory. Articles in the first part cover pure singularity theory: invariants, classification theory, and Milnor fibres. Articles in the second part cover singularities in topology and differential geometry, as well as algebraic geometry and bifurcation theory: Artin-Greenberg function of a plane curve singularity, metric theory of singularities, symplectic singularities, cobordisms of fold maps, Goursat distributions, sections of analytic varieties, Vassiliev invariants, projections of hypersurfaces, and linearity of the Jacobian ideal."--P. [4] of cover.


Real And Complex Singularities

Author by : Ana Claudia Nabarro
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume is a collection of papers presented at the XIII International Workshop on Real and Complex Singularities, held from July 27–August 8, 2014, in São Carlos, Brazil, in honor of María del Carmen Romero Fuster's 60th birthday. The volume contains the notes from two mini-courses taught during the workshop: on intersection homology by J.-P. Brasselet, and on non-isolated hypersurface singularities and Lê cycles by D. Massey. The remaining contributions are research articles which cover topics from the foundations of singularity theory (including classification theory and invariants) to topology of singular spaces (links of singularities and semi-algebraic sets), as well as applications to topology (cobordism and Lefschetz fibrations), dynamical systems (Morse-Bott functions) and differential geometry (affine geometry, Gauss-maps, caustics, frontals and non-Euclidean geometries). This book is published in cooperation with Real Sociedad Matemática Española (RSME)


Real And Complex Singularities

Author by : Marcelo José Saia
Languange : en
Publisher by : American Mathematical Soc.
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Description : Fifteen papers from the July 2006 workshop present recent results in singularity, classification, equisingularity, and topology theory. The mathematicians propose a global classification of curves on the symplectic plane, cobordism invariants of fold maps, an index of quadratic differential forms, and a residue theoretical approach to intersection theory. Other topics include conjugate vectors of immersed manifolds, Thom polynomials and Schur functions, obstructions on fundamental groups of plane curve complements, and exotic moduli of Goursat distributions. No index is provided.


Real And Complex Singularities

Author by : Anonim
Languange : en
Publisher by : Unknown
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Real And Complex Singularities

Author by : Jean-Paul Brasselet
Languange : en
Publisher by : Birkhäuser
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Total Read : 28
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Description : This volume collects papers presented at the eighth São Carlos Workshop on Real and Complex Singularities, held at the IML, Marseille, July 2004. Like the workshop, this collection establishes the state of the art and presents new trends, new ideas and new results in all of the branches of singularities. Real and Complex Singularities offers a useful summary of leading ideas in singularity theory, and inspiration for future research.


Real And Complex Singularities

Author by : Ana Claudia Nabarro
Languange : en
Publisher by : Unknown
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Total Read : 25
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On The Topology Of Isolated Singularities In Analytic Spaces

Author by : José Seade
Languange : en
Publisher by : Springer Science & Business Media
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Description : The aim of this book is to give an overview of selected topics on the topology of real and complex isolated singularities, with emphasis on its relations to other branches of geometry and topology. The first chapters are mostly devoted to complex singularities and a myriad of results spread in a vast literature, which are presented here in a unified way, accessible to non-specialists. Among the topics are the fibration theorems of Milnor; the relation with 3-dimensional Lie groups; exotic spheres; spin structures and 3-manifold invariants; the geometry of quadrics and Arnold's theorem which states that the complex projective plane modulo conjugation is the 4-sphere. The second part of the book studies pioneer work about real analytic singularities which arise from the topological and geometric study of holomorphic vector fields and foliations. In the low dimensional case these turn out to be related to fibred links in the 3-sphere defined by meromorphic functions. This provides new methods for constructing manifolds equipped with a rich geometry. The book is largely self-contained and serves a wide audience of graduate students, mathematicians and researchers interested in geometry and topology.


Real And Complex Singularities Oslo 1976

Author by : Navf Symposium in Mathematics Oslo, Norway 1976
Languange : de
Publisher by : Springer
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Description : This volume contains the lectures given at the Nordic Summer School in Mathematics 1976, as well as the papers reported on in the adjoint sym posium. The Summer School was the 9th in the series sponsored by Nordic Research Courses of the Nordic Cultural Commission. The symposium organized in conjunction with the Summer School was made possible through grants from the Norwegian Research Council for Science and Humanities (NA VF). It is definite that the full project could not have succeeded without the support of both organizations, and I would here like to thank the Nordic Cultural Commission and the Norwegian Research Council for making it possible. The present book contains nearly all talks given at the meeting with one notable exception: The elegant exposition of John Mather on the genericity and finite type of the topologically stable maps was not written up in time to be included in the book. The loss is partly made up for by two recent expositions in the Springer Lecture Notes (No. 535 and 552), which, however, both differ from the presentation given at the Summer School. It is to be hoped that Mather's proof will appear ultimately. Finally I take this opportunity to express my gratitude to the staff of the Mathematics Institute, in particular to Mrs Kirkaloff and Mrs Moller.


Real And Complex Singularities

Author by : Anonim
Languange : en
Publisher by : Unknown
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Real And Complex Singularities Oslo 1976

Author by : Per Holm
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 96
Total Download : 904
File Size : 40,5 Mb
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Description : This volume contains the lectures given at the Nordic Summer School in Mathematics 1976, as well as the papers reported on in the adjoint sym posium. The Summer School was the 9th in the series sponsored by Nordic Research Courses of the Nordic Cultural Commission. The symposium organized in conjunction with the Summer School was made possible through grants from the Norwegian Research Council for Science and Humanities (NA VF). It is definite that the full project could not have succeeded without the support of both organizations, and I would here like to thank the Nordic Cultural Commission and the Norwegian Research Council for making it possible. The present book contains nearly all talks given at the meeting with one notable exception: The elegant exposition of John Mather on the genericity and finite type of the topologically stable maps was not written up in time to be included in the book. The loss is partly made up for by two recent expositions in the Springer Lecture Notes (No. 535 and 552), which, however, both differ from the presentation given at the Summer School. It is to be hoped that Mather's proof will appear ultimately. Finally I take this opportunity to express my gratitude to the staff of the Mathematics Institute, in particular to Mrs Kirkaloff and Mrs Moller.


Singularities I

Author by : Dũng Tráng Lê
Languange : en
Publisher by : American Mathematical Soc.
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Description : This is the first part of the Proceedings of the meeting ``School and Workshop on the Geometry and Topology of Singularities'', held in Cuernavaca, Mexico, from January 8th to 26th of 2007, in celebration of the 60th Birthday of Le Dung Trang. This volume contains fourteen cutting-edge research articles on algebraic and analytic aspects of singularities of spaces and maps. By reading this volume, and the accompanying volume on geometric and topological aspects of singularities, the reader should gain an appreciation for the depth, breadth, and beauty of the subject, and also find a rich source of questions and problems for future study.


Singularity Theory I

Author by : V.I. Arnold
Languange : en
Publisher by : Springer Science & Business Media
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Description : This is a compact guide to the principles and main applications of Singularity Theory by one of the world’s top research groups. It includes a number of new results as well as a carefully prepared and extensive bibliography that makes it easy to find the necessary details. It’s ideal for any mathematician or physicist interested in modern mathematical analysis.