By Jonathan A. Barmak

This quantity bargains with the idea of finite topological areas and its

relationship with the homotopy and easy homotopy conception 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 tools built during this manuscript are used to review 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 truly is intended

for topologists and combinatorialists, however it is usually instructed for

advanced undergraduate scholars and graduate scholars with a modest

knowledge of Algebraic Topology.