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Mathematics - Geometry & Topology | Algebraic Topology of Finite Topological Spaces and Applications

Algebraic Topology of Finite Topological Spaces and Applications

Series: Lecture Notes in Mathematics, Vol. 2032

Barmak, Jonathan A.

2011, XVII, 170p. 35 illus..

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  • It is the first complete exposition of the topic
  • Has applications to the study of two long-standing conjectures
  • It is self-contained
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.

Content Level » Research

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

Related subjects » Algebra - Geometry & Topology

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