Algebraic topology of finite topological spaces and applications / Jonathan A. Barmak

Auteur: Barmak, Jonathan A. - AuteurType de document: MonographieCollection: Lecture notes in mathematics ; 2032Langue: anglaisPays: AllemagneÉditeur: Berlin : Springer, cop. 2011Description: 1 vol. (XVII-170 p.) : fig. ; 24 cm ISBN: 9783642220029 ; br. Résumé: 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. (Source : Springer).Bibliographie: Bibliogr. p. 161-164. Index.Thèse: Texte remanié de : PhD Thesis en mathematics, soutenue en 2009, organisme : Universidad de Buenos Aires Sujets MSC: 55-02 Algebraic topology -- Research exposition (monographs, survey articles)
05E45 Combinatorics -- Algebraic combinatorics -- Combinatorial aspects of simplicial complexes
06A07 Order, lattices, ordered algebraic structures -- Ordered sets -- Combinatorics of partially ordered sets
54F05 General topology -- Special properties -- Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
55P15 Algebraic topology -- Homotopy theory -- Classification of homotopy type
55U05 Algebraic topology -- Applied homological algebra and category theory -- Abstract complexes
57Q10 Manifolds and cell complexes -- PL-topology -- Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc
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Bibliogr. p. 161-164. Index

Texte remanié de : PhD Thesis mathematics 2009 Universidad de Buenos Aires

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. (Source : Springer)

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