Spaces of Homotopy Self-Equivalences: A Survey

John W. Rutter (auth.)3540631038, 9783540631033

This survey covers groups of homotopy self-equivalence classes of topological spaces, and the homotopy type of spaces of homotopy self-equivalences. For manifolds, the full group of equivalences and the mapping class group are compared, as are the corresponding spaces. Included are methods of calculation, numerous calculations, finite generation results, Whitehead torsion and other areas. Some 330 references are given. The book assumes familiarity with cell complexes, homology and homotopy. Graduate students and established researchers can use it for learning, for reference, and to determine the current state of knowledge.

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Table of contents :
Preliminaries….Pages 1-3
Building blocks….Pages 4-6
Representations: homology and homotopy….Pages 7-10
Surfaces….Pages 11-18
Generators: surface, modular groups….Pages 19-27
Manifolds of dimension three or more….Pages 28-33
ɛ * ( X ) not finitely generated….Pages 34-35
Localization….Pages 36-39
ɛ * ( X ) finitely presented, nilpotent….Pages 40-43
L-R duality….Pages 44-44
Cellular/homology complexes: methods….Pages 45-53
Cellular, homology complexes: calculations….Pages 54-62
Non-1-connected postnikov: methods….Pages 63-73
Homotopy systems, chain complexes….Pages 74-79
Non-1-connected spaces: calculations….Pages 80-93
Whitehead torsion, simple homotopy….Pages 94-97
Unions and products….Pages 98-107
Group theoretic properties….Pages 108-112
Homotopy type, homotopy groups….Pages 113-120
Homotopy automorphisms of H -spaces….Pages 121-123
Fibre and equivariant HE’s….Pages 124-129
Applications….Pages 130-133