Surgery on Compact Manifolds

Name: Surgery on Compact Manifolds
Price: 135.34 USD
Availability: InStock
ISBN: 9780821809426

ISBN-10: 0821809423

ISBN-13: 9780821809426

Edition: 2nd 1999 (Revised)

Authors: C. T. C. Wall, A. Ranicki

List price: $77.00

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The publication of this book in 1970 marked the culmination of a particularly exciting period in the history of the topology of manifolds. The world of high-dimensional manifolds had been opened up to the classification methods of algebraic topology by Thom's work in 1952 on transversality and cobordism, the signature theorem of Hirzebruch in 1954, and by the discovery of exotic spheres by Milnor in 1956. In the 1960s, there had been an explosive growth of interest in the surgery method of understanding the homotopy types of manifolds (initially in the differentiable category), including results such as the h-cobordism theory of Smale (1960), the classification of exotic spheres by Kervaire…

Book details

List price: $77.00
Edition: 2nd
Copyright year: 1999
Publisher: American Mathematical Society
Publication date: 3/30/1999
Binding: Hardcover
Pages: 302
Size: 7.25" wide x 10.50" long x 1.00" tall
Weight: 1.694
Language: English



Preliminaries: Note on conventions


Basic homotopy notions Surgery below the middle dimension


Appendix: Applications Simple Poincare complexes


The main theorem: Statement of results


An important special case


The even-dimensional case


The odd-dimensional case


The bounded odd-dimensional case


The bounded even-dimensional case


Completion of the proof Patterns of application: Manifold structures on Poincare complexes


Applications to submanifolds Submanifolds: Other techniques


Separating submanifolds Two-sided submanifolds One-sided submanifolds


Calculations and applications: Calculations: Surgery obstruction groups


Calculations: The surgery obstructions


Applications: Free actions on spheres


General remarks An extension of the Atiyah-Singer $G$-signature theorem


Free actions of $S^1$ Fake projective spaces (real) Fake lens spaces


Applications: Free uniform actions on euclidean space


Fake tori Polycyclic groups


Applications to 4-manifolds Postscript: Further ideas and suggestions: Recent work


function space methods Topological manifolds


Poincare embeddings Homotopy and simple homotopy


Further calculations Sullivan's results


Reformulations of the algebra Rational surgery


References


Index