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Algebraic Topology of Finite Topological Spaces and Applications
Anglais
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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.
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