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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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Bibliographic Details
Main Author: Barmak, Jonathan A.
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2011, 2011
Edition:1st ed. 2011
Series:Lecture Notes in Mathematics
Subjects:
Complex Manifolds
Convex And Discrete Geometry
Discrete Mathematics
Combinatorics
Convex Geometry 
Order, Lattices, Ordered Algebraic Structures
Manifolds And Cell Complexes (incl. Diff.topology)
Algebraic Topology
Algebra
Manifolds (mathematics)
Discrete Geometry
Ordered Algebraic Structures
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • 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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