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101 0 $aeng
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182   $cc$2rdamedia
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200 10$aAlgebraic Topology of Finite Topological Spaces and Applications$b[electronic resource] /$fby Jonathan A. Barmak
205   $a1st ed. 2011.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2011.
215   $a1 online resource (XVII, 170p. 35 illus.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2032
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-642-22002-9 
320   $aIncludes bibliographical references and index.
327   $a1 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.
330   $aThis volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillen?s conjecture on the poset of p-subgroups of a finite group and the Andrews-Curtis conjecture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It is intended for topologists and combinatorialists, but it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v2032
606   $aAlgebraic topology
606   $aCombinatorics
606   $aConvex geometry 
606   $aDiscrete geometry
606   $aAlgebra
606   $aOrdered algebraic structures
606   $aManifolds (Mathematics)
606   $aComplex manifolds
606   $aDiscrete mathematics
606   $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019
606   $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010
606   $aConvex and Discrete Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21014
606   $aOrder, Lattices, Ordered Algebraic Structures$3https://scigraph.springernature.com/ontologies/product-market-codes/M11124
606   $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027
606   $aDiscrete Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29000
615  0$aAlgebraic topology.
615  0$aCombinatorics.
615  0$aConvex geometry .
615  0$aDiscrete geometry.
615  0$aAlgebra.
615  0$aOrdered algebraic structures.
615  0$aManifolds (Mathematics).
615  0$aComplex manifolds.
615  0$aDiscrete mathematics.
615 14$aAlgebraic Topology.
615 24$aCombinatorics.
615 24$aConvex and Discrete Geometry.
615 24$aOrder, Lattices, Ordered Algebraic Structures.
615 24$aManifolds and Cell Complexes (incl. Diff.Topology).
615 24$aDiscrete Mathematics.
676   $a514.2
700   $aBarmak$b Jonathan A$4aut$4http://id.loc.gov/vocabulary/relators/aut$0478960
906   $aBOOK
912   $a996466642803316
996   $aAlgebraic topology of finite topological spaces and applications$9261796
997   $aUNISA