Algebraic L Theory And Topological Manifolds
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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.
Algebraic L Theory And Topological Manifolds
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Author : Andrew Ranicki
language : en
Publisher:
Release Date : 1991
Algebraic L Theory And Topological Manifolds 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 1991 with categories.
Algebraic L Theory And Topological Manifolds
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Author : A. A. Ranicki
language : en
Publisher: Cambridge University Press
Release Date : 2008-01-21
Algebraic L Theory And Topological Manifolds written by A. A. 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 2008-01-21 with Mathematics categories.
This book presents the definitive account of the applications of this algebra to the surgery classification of topological manifolds. The central result is the identification of a manifold structure in the homotopy type of a Poincaré duality space with a local quadratic structure in the chain homotopy type of the universal cover. The difference between the homotopy types of manifolds and Poincaré duality spaces is identified with the fibre of the algebraic L-theory assembly map, which passes from local to global quadratic duality structures on chain complexes. The algebraic L-theory assembly map is used to give a purely algebraic formulation of the Novikov conjectures on the homotopy invariance of the higher signatures; any other formulation necessarily factors through this one.
Algebraic And Geometric Surgery
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Author : Andrew Ranicki
language : en
Publisher: Oxford University Press
Release Date : 2002
Algebraic And Geometric Surgery written by Andrew Ranicki and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 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.
Lower K And L Theory
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Author : Andrew Ranicki
language : en
Publisher: Cambridge University Press
Release Date : 1992-05-21
Lower K And L Theory 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 1992-05-21 with Mathematics categories.
This is the first unified treatment in book form of the lower K-groups of Bass and the lower L-groups of the author.
Differential Forms In Algebraic Topology
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Author : Raoul Bott
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Differential Forms In Algebraic Topology written by Raoul Bott and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.
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 categories.
An Introduction To Manifolds
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Author : Loring W. Tu
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-05
An Introduction To Manifolds written by Loring W. Tu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-05 with Mathematics categories.
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
Surgery On Compact Manifolds
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Author : Charles Terence Clegg Wall
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Surgery On Compact Manifolds written by Charles Terence Clegg Wall and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
The publication of this book in 1970 marked the culmination of a period in the history of the topology of manifolds. This edition, based on the original text, is supplemented by notes on subsequent developments and updated references and commentaries.
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Author :
language : en
Publisher: World Scientific
Release Date :
written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.