Algebraic topology of finite topological spaces and applications
著者
書誌事項
Algebraic topology of finite topological spaces and applications
（Lecture notes in mathematics, 2032）
Springer, c2011
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注記
Rev. version of author's thesis (Ph.D.)--Universidad de Buenos Aires, 2009
Includes bibliographical references (p. 161-164) and index
内容説明・目次
内容説明
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.
目次
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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