Involutions on Manifolds
This book contains the results of work done during the years 1967-1970 on fixed-point-free involutions on manifolds, and is an enlarged version of the author's doctoral dissertation [54J written under the direction of Professor William Browder. The subject of fixed-paint-free involutions, as pa...
| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1971, 1971
|
| Edition: | 1st ed. 1971 |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics
|
| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 0 Notation, Conventions, Preliminaries
- I The Browder-Livesay Invariants
- I.1 Involutions of Spheres
- I.2 Involutions of Simply Connected Manifolds
- II Realization of the Browder-Livesay Invariants
- II.1 The Realization Theorem
- II.2 Constructions with Involutions
- II.3 Proof of Theorem II.1-D
- II.4 Proof of Theorem II.1-A
- II.5 Homology 3-Spheres
- II.6 Manifolds with the Same Regular Homotopy Type as Line Bundles over Projective Spaces
- II.7 Invariant Codimension 2 Spheres
- III Relations with Non-simply-connected Surgery Obstructions
- III.1 Normal Invariants
- III.2 Non-simply-connected Surgery Obstructions
- III.3 Relations with the Browder-Livesay Invariants
- IV Combinatorial Classification of Involutions
- IV.1 Some Maps and Exact Sequences
- IV.2 Computation of [Pn, G/PL]
- IV.3 The Classification Theorem
- IV.4 Another Relation with Non-simply-connected Surgery Obstructions
- IV.5 On the Topological Classification of Involutions
- V Smooth Involutions
- V.1 General Remarks on Smooth Involutions of Spheres
- V.2 Normal Invariants and Browder-Livesay Invariants
- V.3 Differentiable Structure of Spheres and Other Double Coverings
- V.4 Proof of Theorem II.1-B, Smooth Case
- V.5 Involutions and the Generalized Kervaire Invariant
- V.6 Smooth Involutions of Spheres of Low Dimension
- V.7 Action of ?n(??) (After Browder)
- V.8 How to Prove ? = ?
- VI Codimension 2 Invariant Spheres
- VI.1 Invariant vs. Characteristic Spheres
- VI.2 Applications
- VI.3 Knotted and Unknotted Codimension 2 Invariant Spheres
- VI.4 Cobordism Classes of Invariant Knots
- Some Unsolved Problems
- References
- List of Symbols