Surgery on compact manifolds / C.T.C. Wall.

Format:

Book

Author/Creator:

Wall, C. T. C. (Charles Terence Clegg)

Contributor:

Ranicki, Andrew, 1948-

Series:

Mathematical surveys and monographs ; no. 69.

Mathematical surveys and monographs, 0076-5376 ; v. 69

Language:

English

Subjects (All):

Manifolds (Mathematics).

Surgery (Topology).

Physical Description:

xv, 302 pages : illustrations ; 27 cm.

Edition:

Second edition / edited by A.A. Ranicki.

Place of Publication:

Providence, R.I. : American Mathematical Society, [1999]

Contents:

0. Basic homotopy notions 3

1. Surgery below the middle dimension 8

1A. Appendix: applications 17

2. Simple Poincare complexes 21

Part 1 The main theorem

3. Statement of results 32

4. An important special case 39

5. The even-dimensional case 44

6. The odd-dimensional case 57

7. The bounded odd-dimensional case 74

8. The bounded even-dimensional case 82

9. Completion of the proof 91

Part 2 Patterns of application

10. Manifold structures on Poincare complexes 106

11. Applications to submanifolds 118

12. Submanifolds: other techniques 138

12A. Separating submanifolds 142

12B. Two-sided submanifolds 149

12C. One-sided submanifolds 155

Part 3 Calculations and applications

13A. Calculations: surgery obstruction groups 172

13B. Calculations: the surgery obstructions 185

14. Applications: free actions on spheres 195

14A. General remarks 195

14B. An extension of the Atiyah-Singer G-signature theorem 199

14C. Free actions of S[superscript 1] 202

14D. Fake projective spaces (real) 206

14E Fake lens spaces 213

15. Applications: free uniform actions on euclidean space 231

15A. Fake tori 232

15B. Polycyclic groups 237

16. Applications to 4-manifolds 241

17. Further ideas and suggestions: recent work 250

17A. Function space methods 250

17B. Topological manifolds 254

17C. Poincare embeddings 256

17D. Homotopy and simple homotopy 258

17E. Further calculations 262

17F. Sullivan's results 268

17G. Reformulations of the algebra 272

17H. Rational surgery 278.

Notes:

Includes bibliographical references (pages 285-299) and index.

ISBN:

0821809423

OCLC:

40714643