Algebraic and geometric surgery / Andrew Ranicki.

Format:

Book

Author/Creator:

Ranicki, Andrew, 1948-

Series:

Oxford mathematical monographs.

Oxford science publications.

Oxford mathematical monographs

Oxford science publications

Language:

English

Subjects (All):

Surgery (Topology).

Topological manifolds.

Physical Description:

1 online resource (386 p.)

Place of Publication:

Oxford : Clarendon Press ; New York : Oxford University Press, 2002.

Language Note:

English

Summary:

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.

Contents:

PREFACE; Contents; 1 The surgery classification of manifolds; 2 Manifolds; 2.1 Differentiable manifolds; 2.2 Surgery; 2.3 Morse theory; 2.4 Handles; 3 Homotopy and homology; 3.1 Homotopy; 3.2 Homology; 4 Poincaré duality; 4.1 Poincaré duality; 4.2 The homotopy and homology effects of surgery; 4.3 Surfaces; 4.4 Rings with involution; 4.5 Universal Poincaré duality; 5 Bundles; 5.1 Fibre bundles and fibrations; 5.2 Vector bundles; 5.3 The tangent and normal bundles; 5.4 Surgery and bundles; 5.5 The Hopf invariant and the J-homomorphism; 6 Cobordism theory; 6.1 Cobordism and transversality

6.2 Framed cobordism6.3 Unoriented and oriented cobordism; 6.4 Signature; 7 Embeddings, immersions, and singularities; 7.1 The Whitney Immersion and Embedding Theorems; 7.2 Algebraic and geometric intersections; 7.3 The Whitney trick; 7.4 The Smale-Hirsch classification of immersions; 7.5 Singularities; 8 Whitehead torsion; 8.1 The Whitehead group; 8.2 The h- and s-Cobordism Theorems; 8.3 Lens spaces; 9 Poincaré complexes and spherical fibrations; 9.1 Geometric Poincaré complexes; 9.2 Spherical fibrations; 9.3 The Spivak normal fibration; 9.4 Browder-Novikov theory; 10 Surgery on maps

10.1 Surgery on normal maps10.2 The regular homotopy groups; 10.3 Kernels; 10.4 Surgery below the middle dimension; 10.5 Finite generation; 11 The even-dimensional surgery obstruction; 11.1 Quadratic forms; 11.2 The kernel form; 11.3 Surgery on forms; 11.4 The even-dimensional L-groups; 11.5 The even-dimensional surgery obstruction; 12 The odd-dimensional surgery obstruction; 12.1 Quadratic formations; 12.2 The kernel formation; 12.3 The odd-dimensional L-groups; 12.4 The odd-dimensional surgery obstruction; 12.5 Surgery on formations; 12.6 Linking forms; 13 The structure set

13.1 The structure set13.2 The simple structure set; 13.3 Exotic spheres; 13.4 Surgery obstruction theory; References; Index; A; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; Q; R; S; T; U; V; W; Z

Notes:

Description based upon print version of record.

Description based on print version record.

Includes bibliographical references (p. [361]-365) and index.

ISBN:

0-19-154524-4

1-282-06072-4

9786612060724

OCLC:

316102707