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Algebraic topology of finite topological spaces and applications

Author: Jonathan A Barmak
Publisher: Berlin ; New York : Springer, ©2011.
Series: Lecture notes in mathematics (Springer-Verlag), 2032.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Barmak, Jonathan A.
Algebraic topology of finite topological spaces and applications.
Berlin ; New York : Springer, ©2011
(DLC) 2011934806
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jonathan A Barmak
ISBN: 9783642220036 3642220037 9783642220029 3642220029
OCLC Number: 755904141
Description: 1 online resource (xvii, 170 pages).
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.
Series Title: Lecture notes in mathematics (Springer-Verlag), 2032.
Responsibility: Jonathan A. Barmak.

Abstract:

This volume deals with the theory of finite topological spaces and itsrelationship with the homotopy and simple homotopy theory of polyhedra.  Read more...

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From the reviews:"This book deals with the algebraic topology of finite topological spaces and its applications, and includes well-known results on finite spaces and original results developed by the Read more...

 
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