Spaces Of Homotopy Self-equivalences - A Survey (lecture Notes In Mathematics)

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. Preliminaries -- Building Blocks -- Representations: Homology And Homotopy -- Surfaces -- Generators: Surface, Modular Groups -- Manifolds Of Dimension Three Or More -- * (x) Not Finitely Generated -- Localization -- * (x) Finitely Presented, Nilpotent -- L-r Duality -- Cellular/homology Complexes: Methods -- Cellular, Homology Complexes: Calculations -- Non-1-connected Postnikov: Methods -- Homotopy Systems, Chain Complexes -- Non-1-connected Spaces: Calculations -- Whitehead Torsion, Simple Homotopy -- Unions And Products -- Group Theoretic Properties -- Homotopy Type, Homotopy Groups -- Homotopy Automorphisms Of H-spaces -- Fibre And Equivariant He's -- Applications -- Arithmetics Groups And Commensurability -- Nilpotency, Rank And Group Actions -- References -- List Of Notation -- Index. John W. Rutter. Includes Bibliographical References And Index. 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