One-point reductions of finite spaces, h-regular CW-complexes and collapsibility

JONATHAN ARIEL BARMAK; ELIAS GABRIEL MINIAN

Algebraic & Geometric Topology

Año: 2008 vol. 8 p. 1763 - 1780

1472-2747

We investigate one-point reduction methods of finite topological spaces. These methods allow one to study homotopy theory of cell complexes by means of elementary moves of their finite models. We also introduce the notion of h–regular CW–complex, generalizing the concept of regular CW–complex, and prove that the h–regular CW–complexes, which are a sort of combinatorial-up-to-homotopy objects, are modeled (up to homotopy) by their associated finite spaces. This is accomplished by generalizing a classical result of McCord on simplicial complexes.