Exact Sequences In The Algebraic Theory Of Surgery
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Exact Sequences In The Algebraic Theory Of Surgery
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Author : Andrew Ranicki
language : en
Publisher:
Release Date : 1981
Exact Sequences In The Algebraic Theory Of Surgery written by Andrew Ranicki and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
The Description for this book, Exact Sequences in the Algebraic Theory of Surgery. (MN-26): , will be forthcoming.
A Course On Surgery Theory
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Author : Stanley Chang
language : en
Publisher: Princeton University Press
Release Date : 2021-01-26
A Course On Surgery Theory written by Stanley Chang and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-26 with Mathematics categories.
Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and respected series in science published, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. Book jacket.
Equivariant Surgery Theories And Their Periodicity Properties
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Author : Karl H. Dovermann
language : en
Publisher: Springer
Release Date : 2006-11-14
Equivariant Surgery Theories And Their Periodicity Properties written by Karl H. Dovermann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The theory of surgery on manifolds has been generalized to categories of manifolds with group actions in several different ways. This book discusses some basic properties that such theories have in common. Special emphasis is placed on analogs of the fourfold periodicity theorems in ordinary surgery and the roles of standard general position hypotheses on the strata of manifolds with group actions. The contents of the book presuppose some familiarity with the basic ideas of surgery theory and transformation groups, but no previous knowledge of equivariant surgery is assumed. The book is designed to serve either as an introduction to equivariant surgery theory for advanced graduate students and researchers in related areas, or as an account of the authors' previously unpublished work on periodicity for specialists in surgery theory or transformation groups.
Algebraic L Theory And Topological Manifolds
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Author : Andrew Ranicki
language : en
Publisher: Cambridge University Press
Release Date : 1992-12-10
Algebraic L Theory And Topological Manifolds written by Andrew Ranicki and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-12-10 with Mathematics categories.
Assuming no previous acquaintance with surgery theory and justifying all the algebraic concepts used by their relevance to topology, Dr Ranicki explains the applications of quadratic forms to the classification of topological manifolds, in a unified algebraic framework.
The Geometric Hopf Invariant And Surgery Theory
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Author : Michael Crabb
language : en
Publisher: Springer
Release Date : 2018-01-24
The Geometric Hopf Invariant And Surgery Theory written by Michael Crabb and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-24 with Mathematics categories.
Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists. Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, with many results old and new.
Algebraic And Geometric Surgery
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Author : Andrew Ranicki
language : en
Publisher: Clarendon Press
Release Date : 2002-09-26
Algebraic And Geometric Surgery written by Andrew Ranicki and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-26 with Mathematics categories.
This book is an introduction to surgery theory: the standard classification method for high-dimensional manifolds. It is aimed at graduate students who have already had a basic topology course, and would now like to understand the topology of high-dimensional manifolds. This text contains entry-level accounts of the various prerequisites of both algebra and topology, including basic homotopy and homology, Poincare duality, bundles, cobordism, embeddings, immersions, Whitehead torsion, Poincare complexes, spherical fibrations and quadratic forms and formations. While concentrating on the basic mechanics of surgery, this book includes many worked examples, useful drawings for illustration of the algebra and references for further reading.
Surveys On Surgery Theory Volume 1
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Author : Sylvain Cappell
language : en
Publisher: Princeton University Press
Release Date : 2014-09-08
Surveys On Surgery Theory Volume 1 written by Sylvain Cappell and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-08 with Mathematics categories.
Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. There have been some extraordinary accomplishments in that time, which have led to enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source that surveys surgery theory and its applications. Indeed, no one person could write such a survey. The sixtieth birthday of C. T. C. Wall, one of the leaders of the founding generation of surgery theory, provided an opportunity to rectify the situation and produce a comprehensive book on the subject. Experts have written state-of-the-art reports that will be of broad interest to all those interested in topology, not only graduate students and mathematicians, but mathematical physicists as well. Contributors include J. Milnor, S. Novikov, W. Browder, T. Lance, E. Brown, M. Kreck, J. Klein, M. Davis, J. Davis, I. Hambleton, L. Taylor, C. Stark, E. Pedersen, W. Mio, J. Levine, K. Orr, J. Roe, J. Milgram, and C. Thomas.
Surgery Theory
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Author : Wolfgang Lück
language : en
Publisher: Springer Nature
Release Date : 2024-07-05
Surgery Theory written by Wolfgang Lück and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-05 with Mathematics categories.
This monograph provides a comprehensive introduction to surgery theory, the main tool in the classification of manifolds. Surgery theory was developed to carry out the so-called Surgery Program, a basic strategy to decide whether two closed manifolds are homeomorphic or diffeomorphic. This book provides a detailed explanation of all the ingredients necessary for carrying out the surgery program, as well as an in-depth discussion of the obstructions that arise. The components include the surgery step, the surgery obstruction groups, surgery obstructions, and the surgery exact sequence. This machinery is applied to homotopy spheres, the classification of certain fake spaces, and topological rigidity. The book also offers a detailed description of Ranicki's chain complex version, complete with a proof of its equivalence to the classical approach developed by Browder, Novikov, Sullivan, and Wall. This book has been written for learning surgery theory and includes numerous exercises. With full proofs and detailed explanations, it also provides an invaluable reference for working mathematicians. Each chapter has been designed to be largely self-contained and includes a guide to help readers navigate the material, making the book highly suitable for lecture courses, seminars, and reading courses.
Surveys On Surgery Theory Volume 2
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Author : Sylvain Cappell
language : en
Publisher: Princeton University Press
Release Date : 2014-09-08
Surveys On Surgery Theory Volume 2 written by Sylvain Cappell and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-08 with Mathematics categories.
Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. The sixtieth birthday (on December 14, 1996) of C.T.C. Wall, a leading member of the subject's founding generation, led the editors of this volume to reflect on the extraordinary accomplishments of surgery theory as well as its current enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source surveying surgery theory and its applications. Because no one person could write such a survey, the editors asked a variety of experts to report on the areas of current interest. This is the second of two volumes resulting from that collective effort. It will be useful to topologists, to other interested researchers, and to advanced students. The topics covered include current applications of surgery, Wall's finiteness obstruction, algebraic surgery, automorphisms and embeddings of manifolds, surgery theoretic methods for the study of group actions and stratified spaces, metrics of positive scalar curvature, and surgery in dimension four. In addition to the editors, the contributors are S. Ferry, M. Weiss, B. Williams, T. Goodwillie, J. Klein, S. Weinberger, B. Hughes, S. Stolz, R. Kirby, L. Taylor, and F. Quinn.
Novikov Conjectures Index Theorems And Rigidity Volume 1
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Author : Steven C. Ferry
language : en
Publisher: Cambridge University Press
Release Date : 1995-11-23
Novikov Conjectures Index Theorems And Rigidity Volume 1 written by Steven C. Ferry and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-11-23 with Mathematics categories.
These volumes are the outgrowth of a conference held at the Mathematisches Forschungsinstitut Oberwolfach (Germany) on the subject of 'Novikov Conjectures, Index Theorems and Rigidity'.