Algebraic Topology of Finite Topological Spaces and Applications

This volume deals with the theory of finite topological spaces and itsrelationship with the homotopy and simple homotopy theory of polyhedra.The interaction between their intrinsic combinatorial and topologicalstructures makes finite spaces a useful tool for studying problems inTopology, Algebra and Geometry from a new perspective. In particular,the methods developed in this manuscript are used to study Quillen'sconjecture on the poset of p-subgroups of a finite group and theAndrews-Curtis conje