Algebraic Topology of Finite Topological Spaces and Applications

This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra...

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Détails bibliographiques
Cote:Libro Electrónico
Auteur principal: Barmak, Jonathan A. (Auteur)
Collectivité auteur: SpringerLink (Online service)
Format: Électronique eBook
Langue:Inglés
Publié: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2011.
Édition:1st ed. 2011.
Collection:Lecture Notes in Mathematics, 2032
Sujets:
Algebraic topology.
Discrete mathematics.
Convex geometry .
Discrete geometry.
Algebra.
Manifolds (Mathematics).
Algebraic Topology.
Discrete Mathematics.
Convex and Discrete Geometry.
Order, Lattices, Ordered Algebraic Structures.
Manifolds and Cell Complexes.
Accès en ligne:Texto Completo
Table des matières:
  • 1 Preliminaries
  • 2 Basic topological properties of finite spaces
  • 3 Minimal finite models
  • 4 Simple homotopy types and finite spaces
  • 5 Strong homotopy types
  • 6 Methods of reduction
  • 7 h-regular complexes and quotients
  • 8 Group actions and a conjecture of Quillen
  • 9 Reduced lattices
  • 10 Fixed points and the Lefschetz number
  • 11 The Andrews-Curtis conjecture.

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