00000cmm a22000004a 4500 UP-99796217611212057 Buklod 20230215085534.0 m go j cr cn |||aaaaa 110822s2011 xx u | eng d 9783642220036 (eBook) 3642220037 (eBook) (iLib)UPD-00214608213 DLC DML eng DMLUC QA 611.3 B37 2011eb Barmak, Jonathan A Algebraic topology of finite topological spaces and applications [electronic resource] Jonathan A. Barmak. Berlin New York Springer c2011. 1 online resource (xvii, 170 p.) ill. Lecture Notes in Mathematics 2032 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. IP-based subscription, access limited to within on-campus computer network. Access via Electronic Resources of the UPD University Library Website. 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 Quillens 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. Electronic reproduction. New York SpringerLink 2011. Available via World Wide Web through SpringerLink. Topological spaces. Algebraic topology. Homotopy theory. Partially ordered sets. Electronic books. SpringerLink (Online service). Electronic Resource Available for University of the Philippines Diliman via SpringerLink. Click here to access http://link.springer.com/book/10.1007/978-3-642-22003-6 FO Monograph UPD DMLR Electronic Resource