Spaces of Homotopy Self-Equivalences - A Survey

• Main Author: Rutter, John W. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1997.
• Edition: 1st ed. 1997.
• Series: Lecture Notes in Mathematics, 1662
• Subjects: Algebraic topology.; Algebraic Topology.

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 calcul...

Table of Contents:

• 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.