Algebraic Topology of Finite Topological Spaces and Applications

  • Jonathan A. Barmak

Part of the Lecture Notes in Mathematics book series (LNM, volume 2032)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Jonathan A. Barmak
    Pages 1-18
  3. Jonathan A. Barmak
    Pages 19-35
  4. Jonathan A. Barmak
    Pages 37-47
  5. Jonathan A. Barmak
    Pages 49-72
  6. Jonathan A. Barmak
    Pages 73-84
  7. Jonathan A. Barmak
    Pages 85-91
  8. Jonathan A. Barmak
    Pages 93-104
  9. Jonathan A. Barmak
    Pages 105-120
  10. Jonathan A. Barmak
    Pages 121-127
  11. Jonathan A. Barmak
    Pages 129-135
  12. Jonathan A. Barmak
    Pages 137-150
  13. Back Matter
    Pages 151-170

About this book

Introduction

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 and Geometry from a new perspective. In particular,
the methods developed in this manuscript are used to study Quillen’s
conjecture on the poset of p-subgroups of a finite group and the
Andrews-Curtis conjecture on the 3-deformability of contractible
two-dimensional complexes.
This self-contained work constitutes the first detailed
exposition on the algebraic topology of finite spaces. It is intended
for topologists and combinatorialists, but it is also recommended for
advanced undergraduate students and graduate students with a modest
knowledge of Algebraic Topology.

Keywords

55-XX; 05-XX; 52-XX ; 06-XX ; 57-XX Collapses Finite topological spaces Homotopy and simple homotopy types Weak homotopy equivalences

Authors and affiliations

  • Jonathan A. Barmak
    • 1
  1. 1.Fac. de Cs. Exactas y Naturales, Dept. de MatemáticaUniversidad de Buenos AiresCiudad de Buenos AiresArgentina

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-22003-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-22002-9
  • Online ISBN 978-3-642-22003-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book