Algebraic Topology of Finite Topological Spaces and Applications

Released on by Jonathan A. Barmak
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  • Algebraic Topology of Finite Topological Spaces and Applications Book Detail

  • Author : Jonathan A. Barmak
  • Release Date : 2011-08-24
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 184
  • ISBN 13 : 3642220029
  • File Size : 7,7 MB
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Algebraic Topology of Finite Topological Spaces and Applications by Jonathan A. Barmak PDF Summary

Book Description: 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.

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