03046nam 2200577 a 450 991048442230332120200520144314.09783642220036364222003710.1007/978-3-642-22003-6(CKB)3440000000000120(DE-He213)978-3-642-22003-6(SSID)ssj0000595561(PQKBManifestationID)11373139(PQKBTitleCode)TC0000595561(PQKBWorkID)10555307(PQKB)11724779(MiAaPQ)EBC3067142(PPN)156316404(EXLCZ)99344000000000012020110720d2011 uy 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierAlgebraic topology of finite topological spaces and applications /Jonathan A. Barmak1st ed. 2011.New York Springer20111 online resource (XVII, 170p. 35 illus.) Lecture notes in mathematics,0075-8434 ;2032Bibliographic Level Mode of Issuance: Monograph9783642220029 3642220029 Includes bibliographical references and index.1 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.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.Lecture notes in mathematics (Springer-Verlag) ;2032.Algebraic topologyTopological spacesAlgebraic topology.Topological spaces.514.2Barmak Jonathan A478960MiAaPQMiAaPQMiAaPQBOOK9910484422303321Algebraic topology of finite topological spaces and applications261796UNINA