Surgery on Compact Manifolds

Surgery on Compact Manifolds
Title Surgery on Compact Manifolds PDF eBook
Author Charles Terence Clegg Wall
Publisher American Mathematical Soc.
Pages 321
Release 1999
Genre Mathematics
ISBN 0821809423

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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.

Surgery on Simply-Connected Manifolds

Surgery on Simply-Connected Manifolds
Title Surgery on Simply-Connected Manifolds PDF eBook
Author William Browder
Publisher Springer Science & Business Media
Pages 141
Release 2012-12-06
Genre Mathematics
ISBN 364250020X

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This book is an exposition of the technique of surgery on simply-connected smooth manifolds. Systematic study of differentiable manifolds using these ideas was begun by Milnor [45] and Wallace [68] and developed extensively in the last ten years. It is now possible to give a reasonably complete theory of simply-connected manifolds of dimension ~ 5 using this approach and that is what I will try to begin here. The emphasis has been placed on stating and proving the general results necessary to apply this method in various contexts. In Chapter II, these results are stated, and then applications are given to characterizing the homotopy type of differentiable manifolds and classifying manifolds within a given homotopy type. This theory was first extensively developed in Kervaire and Milnor [34] in the case of homotopy spheres, globalized by S. P. Novikov [49] and the author [6] for closed 1-connected manifolds, and extended to the bounded case by Wall [65] and Golo [23]. The thesis of Sullivan [62] reformed the theory in an elegant way in terms of classifying spaces.

Surgery on Contact 3-Manifolds and Stein Surfaces

Surgery on Contact 3-Manifolds and Stein Surfaces
Title Surgery on Contact 3-Manifolds and Stein Surfaces PDF eBook
Author Burak Ozbagci
Publisher Springer Science & Business Media
Pages 279
Release 2013-03-09
Genre Mathematics
ISBN 366210167X

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This book is about an investigation of recent developments in the field of sympletic and contact structures on four- and three-dimensional manifolds from a topologist’s point of view. In it, two main issues are addressed: what kind of sympletic and contact structures we can construct via surgery theory and what kind of sympletic and contact structures are not allowed via gauge theory and the newly invented Heegaard-Floer theory.

Algebraic and Geometric Surgery

Algebraic and Geometric Surgery
Title Algebraic and Geometric Surgery PDF eBook
Author Andrew Ranicki
Publisher Oxford University Press
Pages 396
Release 2002
Genre Mathematics
ISBN 9780198509240

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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, co-bordism, 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.

Algebraic L-theory and Topological Manifolds

Algebraic L-theory and Topological Manifolds
Title Algebraic L-theory and Topological Manifolds PDF eBook
Author Andrew Ranicki
Publisher Cambridge University Press
Pages 372
Release 1992-12-10
Genre Mathematics
ISBN 9780521420242

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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.

An Introduction to Manifolds

An Introduction to Manifolds
Title An Introduction to Manifolds PDF eBook
Author Loring W. Tu
Publisher Springer Science & Business Media
Pages 426
Release 2010-10-05
Genre Mathematics
ISBN 1441974008

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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'.

Exact Sequences in the Algebraic Theory of Surgery

Exact Sequences in the Algebraic Theory of Surgery
Title Exact Sequences in the Algebraic Theory of Surgery PDF eBook
Author Andrew Ranicki
Publisher
Pages 863
Release 1981
Genre Mathematics
ISBN 9780691082769

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The Description for this book, Exact Sequences in the Algebraic Theory of Surgery. (MN-26): , will be forthcoming.