Algebraic Topology of Finite Topological Spaces and Applications

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. (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
Series:Lecture Notes in Mathematics, 2032
Subjects:
Mathematics.
Algebra.
Ordered algebraic structures.
Convex geometry.
Discrete geometry.
Algebraic topology.
Manifolds (Mathematics).
Complex manifolds.
Discrete mathematics.
Combinatorics.
Algebraic Topology.
Convex and Discrete Geometry.
Order, Lattices, Ordered Algebraic Structures.
Manifolds and Cell Complexes (incl. Diff.Topology).
Discrete Mathematics.
Online Access:Full Text via HEAL-Link
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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