Algebraic Topology of Finite Topological Spaces and by Jonathan A. Barmak

By Jonathan A. Barmak

This quantity bargains with the idea of finite topological areas and its
relationship with the homotopy and easy homotopy idea of polyhedra.
The interplay among their intrinsic combinatorial and topological
structures makes finite areas a useful gizmo for learning difficulties in
Topology, Algebra and Geometry from a brand new viewpoint. In particular,
the equipment built during this manuscript are used to check Quillen's
conjecture at the poset of p-subgroups of a finite crew and the
Andrews-Curtis conjecture at the 3-deformability of contractible
two-dimensional complexes.
This self-contained paintings constitutes the 1st detailed
exposition at the algebraic topology of finite areas. it's intended
for topologists and combinatorialists, however it is additionally urged for
advanced undergraduate scholars and graduate scholars with a modest
knowledge of Algebraic Topology.

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