A Course on Surgery Theory

Name: A Course on Surgery Theory | (AMS-211)
Brand: Princeton University Press
Price: 84.99 EUR
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(AMS-211)

Stanley Chang Shmuel Weinberger(Autor*in)

Princeton University Press

1. Auflage

Erschienen am 26. Januar 2021

472 Seiten

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978-0-691-20035-4 (ISBN)

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Inhalt

Cover
Title
Copyright
Contents
List of Figures
Preface
Introduction
1 The characterization of homotopy types
1.1 A review of surgery
1.2 Executing surgery
1.3 The p-p theorem and its applications
1.4 Propagation of group actions
1.5 Wall Chapter 9
1.6 Algebraic surgery theory
2 Some calculations of L-groups
2.1 Calculating L*(Z[e])
2.2 Elementary Witt theory
2.3 L-theory of finite groups
2.4 Odd L-groups and the Ranicki-Rothenberg sequence
2.5 Transfer and Dress induction
2.6 Squares
2.7 Using splitting theorems
3 Classical surgery theory
3.1 Low dimensions and smoothing theory
3.2 The homotopy groups of F/PL
3.3 Some PL and Diff examples
3.4 The homotopy type of F/PL
3.5 Finite H-spaces
3.6 PL tori
3.7 The Kirby-Siebenmann invariant
3.8 Nonrigidity of nonuniform arithmetic manifolds
4 Topological surgery and surgery spaces
4.1 Beginning the spacification
4.2 The surgery problem
4.3 Blocked surgery
4.4 Surgery spectra
4.5 Periodicity of structure sets
4.6 Smooth structures
5 Applications of the assembly map
5.1 The Borel conjecture and related questions
5.2 Applications of periodicity and functoriality
5.3 Automatic variability of characteristic classes
6 Beyond characteristic classes
6.1 A secondary signature invariant
6.2 Manifolds with fundamental group Z2
6.3 General splittability
6.4 Connected sums of projective spaces
6.5 Lens spaces
6.6 The topological space form problem
6.7 Oozing problem
6.8 Introduction to the Farrell-Jones conjecture
6.9 Propagation of group actions on closed manifolds
7 Flat and almost flat manifolds
7.1 The a-approximation theorem
7.2 Flat manifolds
7.3 Almost flat manifolds
8 Other surgery theories
8.1 Smooth surgery without usual normal data
8.2 Local surgery
8.3 Homology surgery
8.4 Proper and bounded surgery
8.5 Controlled surgery
8.6 Homology manifolds
8.7 Stratified surgery
Appendix A: Some background in algebraic topology
A.1 Obstruction theory
A.2 Principal bundles and characteristic classes
A.3 Generalized homology theories
A.4 Localization
A.5 Whitehead torsion
Appendix B: Geometric preliminaries
B.1 The smooth category
B.2 The PL category
B.3 The topological category
List of Symbols
Bibliography
Index

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