Algebraic topology of finite topological spaces and applications /

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Bibliographic Details
Author / Creator:	Barmak, Jonathan A.
Imprint:	Berlin ; New York : Springer, ©2011.
Description:	1 online resource (xvii, 170 pages).
Language:	English
Series:	Lecture notes in mathematics ; 2032 Lecture notes in mathematics (Springer-Verlag) ; 2032.
Subject:	Algebraic topology. Algebraic topology.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11076053

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ISBN:	9783642220036 3642220037 9783642220029 3642220029
Notes:	Includes bibliographical references (pages 161-164) and index.
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 Quillen{u2019}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.

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