LEADER 02991nam 2200553 a 450 001 9910484422303321 005 20200520144314.0 010 $a3-642-22003-7 024 7 $a10.1007/978-3-642-22003-6 035 $a(CKB)3440000000000120 035 $a(DE-He213)978-3-642-22003-6 035 $a(SSID)ssj0000595561 035 $a(PQKBManifestationID)11373139 035 $a(PQKBTitleCode)TC0000595561 035 $a(PQKBWorkID)10555307 035 $a(PQKB)11724779 035 $a(MiAaPQ)EBC3067142 035 $a(PPN)156316404 035 $a(EXLCZ)993440000000000120 100 $a20110720d2011 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAlgebraic topology of finite topological spaces and applications /$fJonathan A. Barmak 205 $a1st ed. 2011. 210 $aNew York $cSpringer$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 (Springer-Verlag) ;$v2032. 606 $aAlgebraic topology 606 $aTopological spaces 615 0$aAlgebraic topology. 615 0$aTopological spaces. 676 $a514.2 700 $aBarmak$b Jonathan A$0478960 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484422303321 996 $aAlgebraic topology of finite topological spaces and applications$9261796 997 $aUNINA