Download or read book Topological Stability of Smooth Mappings written by C.G. Gibson and published by Springer. This book was released on 2006-11-14 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the academic year 1974-75, the Department of Pure Mathematics in the University of Liverpool held a seminar on the topological stability of smooth mappings. The main objective was to piece together a complete proof of the topological stability theorem (conjectured by René Thom in 1960, and proved by John Mather in 1970) for which no published accounts existed. This volume comprises a write-up of the seminar by four of the participants. Any mathematician working in this area is conscious of a debt to the inventiveness of Thom, and to Mather for the technical work which placed much that was conjecture on firm mathematical foundations. The proof presented in these notes follows Thom's indications closely, and requires no more than some familiarity with differential topology and commutative algebra of the reader.
Download or read book Topological Stability of Smooth Mappings written by C. G. Gibson and published by . This book was released on 2014-09-01 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lecture Notes in Mathematics written by and published by . This book was released on 1964 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Complements of Discriminants of Smooth Maps written by V. A. Vasilʹev and published by American Mathematical Soc.. This book was released on 1994 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Up-to-date reference on this exciting area of mathematics * Discusses the wide range of applications in topology, algebraic geometry, and catastrophe theory.
Download or read book Stable Mappings and Their Singularities written by M. Golubitsky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to present to first and second year graduate students a beautiful and relatively accessible field of mathematics-the theory of singu larities of stable differentiable mappings. The study of stable singularities is based on the now classical theories of Hassler Whitney, who determined the generic singularities (or lack of them) of Rn ~ Rm (m ~ 2n - 1) and R2 ~ R2, and Marston Morse, for mappings who studied these singularities for Rn ~ R. It was Rene Thorn who noticed (in the late '50's) that all of these results could be incorporated into one theory. The 1960 Bonn notes of Thom and Harold Levine (reprinted in [42]) gave the first general exposition of this theory. However, these notes preceded the work of Bernard Malgrange [23] on what is now known as the Malgrange Preparation Theorem-which allows the relatively easy computation of normal forms of stable singularities as well as the proof of the main theorem in the subject-and the definitive work of John Mather. More recently, two survey articles have appeared, by Arnold [4] and Wall [53], which have done much to codify the new material; still there is no totally accessible description of this subject for the beginning student. We hope that these notes will partially fill this gap. In writing this manuscript, we have repeatedly cribbed from the sources mentioned above-in particular, the Thom-Levine notes and the six basic papers by Mather.
Download or read book Topology of Singular Fibers of Differentiable Maps written by Osamu Saeki and published by Springer. This book was released on 2004-08-30 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume develops a thorough theory of singular fibers of generic differentiable maps. This is the first work that establishes the foundational framework of the global study of singular differentiable maps of negative codimension from the viewpoint of differential topology. The book contains not only a general theory, but also some explicit examples together with a number of very concrete applications. This is a very interesting subject in differential topology, since it shows a beautiful interplay between the usual theory of singularities of differentiable maps and the geometric topology of manifolds.
Download or read book Handbook of Geometry and Topology of Singularities III written by José Luis Cisneros-Molina and published by Springer Nature. This book was released on 2022-06-06 with total page 822 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I and II, such as, for instance, Zariski’s equisingularity, the interplay between isolated complex surface singularities and 3-manifold theory, stratified Morse theory, constructible sheaves, the topology of the non-critical levels of holomorphic functions, and intersection cohomology. Other chapters bring in new subjects, such as the Thom–Mather theory for maps, characteristic classes for singular varieties, mixed Hodge structures, residues in complex analytic varieties, nearby and vanishing cycles, and more. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
Download or read book Real and Complex Singularities written by Laurentiu Paunescu and published by World Scientific. This book was released on 2007 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Differential Topology written by C. T. C. Wall and published by Cambridge University Press. This book was released on 2016-07-04 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring the full scope of differential topology, this comprehensive account of geometric techniques for studying the topology of smooth manifolds offers a wide perspective on the field. Building up from first principles, concepts of manifolds are introduced, supplemented by thorough appendices giving background on topology and homotopy theory. Deep results are then developed from these foundations through in-depth treatments of the notions of general position and transversality, proper actions of Lie groups, handles (up to the h-cobordism theorem), immersions and embeddings, concluding with the surgery procedure and cobordism theory. Fully illustrated and rigorous in its approach, little prior knowledge is assumed, and yet growing complexity is instilled throughout. This structure gives advanced students and researchers an accessible route into the wide-ranging field of differential topology.
Download or read book Singularities of Mappings written by David Mond and published by Springer Nature. This book was released on 2020-01-23 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first monograph on singularities of mappings for many years, this book provides an introduction to the subject and an account of recent developments concerning the local structure of complex analytic mappings. Part I of the book develops the now classical real C∞ and complex analytic theories jointly. Standard topics such as stability, deformation theory and finite determinacy, are covered in this part. In Part II of the book, the authors focus on the complex case. The treatment is centred around the idea of the "nearby stable object" associated to an unstable map-germ, which includes in particular the images and discriminants of stable perturbations of unstable singularities. This part includes recent research results, bringing the reader up to date on the topic. By focusing on singularities of mappings, rather than spaces, this book provides a necessary addition to the literature. Many examples and exercises, as well as appendices on background material, make it an invaluable guide for graduate students and a key reference for researchers. A number of graduate level courses on singularities of mappings could be based on the material it contains.
Download or read book Real Analytic and Algebraic Singularities written by Toshisumi Fukui and published by CRC Press. This book was released on 1997-12-12 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of papers covering recent progress in a number of areas of singularity theory. Topics include blow analyticity, recent progress in the research on equivalence relations of maps and functions, sufficiency of jets, and the transversality theorem. . Geometric and analytic studies of partial differential equations have been developed independently of one another, but the shock wave solutions appearing in natural phenomena are not well understood. Singularity theory may unify these studies and a survey based on this viewpoint is presented in which a new notion of weak solution is introduced. There are also reports on the recent progress in Zariski's conjecture on multiplicities of hypersurfaces, transcendency of analytic sets and on the topology of weighted homogeneous polynomials. This book will be of particular interest to specialists in singularities, partial differential equations, algebraic geometry and control theory.
Download or read book Singularities and Foliations Geometry Topology and Applications written by Raimundo Nonato Araújo dos Santos and published by Springer. This book was released on 2018-03-21 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Topological Nonlinear Analysis written by Michele Matzeu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological tools in Nonlinear Analysis had a tremendous develop ment during the last few decades. The three main streams of research in this field, Topological Degree, Singularity Theory and Variational Meth ods, have lately become impetuous rivers of scientific investigation. The process is still going on and the achievements in this area are spectacular. A most promising and rapidly developing field of research is the study of the role that symmetries play in nonlinear problems. Symmetries appear in a quite natural way in many problems in physics and in differential or symplectic geometry, such as closed orbits for autonomous Hamiltonian systems, configurations of symmetric elastic plates under pressure, Hopf Bifurcation, Taylor vortices, convective motions of fluids, oscillations of chemical reactions, etc . . . Some of these problems have been tackled recently by different techniques using equivariant versions of Degree, Singularity and Variations. The main purpose of the present volume is to give a survey of some of the most significant achievements obtained by topological methods in Nonlinear Analysis during the last two-three decades. The survey articles presented here reflect the personal taste and points of view of the authors (all of them well-known and distinguished specialists in their own fields) on the subject matter. A common feature of these papers is that of start ing with an historical introductory background of the different disciplines under consideration and climbing up to the heights of the most recent re sults.
Download or read book Singularities written by Jean-Paul Brasselet and published by Cambridge University Press. This book was released on 1994-07-07 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains papers given at the International Singularity Conference held in 1991 at Lille.
Download or read book Singularity Theory written by Bill Bruce and published by Cambridge University Press. This book was released on 1999-06-03 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date survey of research in singularity theory.
Download or read book Medial Skeletal Linking Structures for Multi Region Configurations written by James Damon and published by American Mathematical Soc.. This book was released on 2018-01-16 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider a generic configuration of regions, consisting of a collection of distinct compact regions in which may be either regions with smooth boundaries disjoint from the others or regions which meet on their piecewise smooth boundaries in a generic way. They introduce a skeletal linking structure for the collection of regions which simultaneously captures the regions' individual shapes and geometric properties as well as the “positional geometry” of the collection. The linking structure extends in a minimal way the individual “skeletal structures” on each of the regions. This allows the authors to significantly extend the mathematical methods introduced for single regions to the configuration of regions.
Download or read book The Geometry of Topological Stability written by Andrew Du Plessis and published by . This book was released on 1995-12-07 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to give necessary and sufficient conditions for aCToo map to be CTo-stable: the aim is achieved in a wide range of dimensions via a detailed study of the geometry and topology of many classes of "generic" singularities. Written by internationally renowned authors, the book describes original research, virtually none of which has appeared before in either articles or in book form. The methods developed will stimulate future progress from their application, especially with regard to singularity theory.
