By Jonathan A. Barmak

This quantity offers with the speculation of finite topological areas and its
relationship with the homotopy and straightforward homotopy concept 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 standpoint. In particular,
the equipment built during this manuscript are used to check Quillen's
conjecture at the poset of p-subgroups of a finite workforce 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 truly is intended
for topologists and combinatorialists, however it can be instructed for
advanced undergraduate scholars and graduate scholars with a modest
knowledge of Algebraic Topology.

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Algebraic Topology of Finite Topological Spaces and Applications (Lecture Notes in Mathematics) by Jonathan A. Barmak

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