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001 978-3-642-22003-6
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020 _a9783642220036
_9978-3-642-22003-6
024 7 _a10.1007/978-3-642-22003-6
_2doi
050 4 _aQA612-612.8
072 7 _aPBPD
_2bicssc
072 7 _aMAT038000
_2bisacsh
082 0 4 _a514.2
_223
100 1 _aBarmak, Jonathan A.
_eauthor.
245 1 0 _aAlgebraic Topology of Finite Topological Spaces and Applications
_h[electronic resource] /
_cby Jonathan A. Barmak.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2011.
300 _aXVII, 170p. 35 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2032
505 0 _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.
520 _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.
650 0 _aMathematics.
650 0 _aAlgebra.
650 0 _aCombinatorics.
650 0 _aDiscrete groups.
650 0 _aAlgebraic topology.
650 0 _aCell aggregation
_xMathematics.
650 1 4 _aMathematics.
650 2 4 _aAlgebraic Topology.
650 2 4 _aCombinatorics.
650 2 4 _aConvex and Discrete Geometry.
650 2 4 _aOrder, Lattices, Ordered Algebraic Structures.
650 2 4 _aManifolds and Cell Complexes (incl. Diff.Topology).
650 2 4 _aDiscrete Mathematics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642220029
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2032
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-22003-6
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c108112
_d108112