One-point reductions of finite spaces, h-regular CW-complexes and collapsibility
Algebraic Topology
2014-10-01 v2 Combinatorics
Geometric Topology
Abstract
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.
Keywords
Cite
@article{arxiv.0801.0007,
title = {One-point reductions of finite spaces, h-regular CW-complexes and collapsibility},
author = {Jonathan Ariel Barmak and Elias Gabriel Minian},
journal= {arXiv preprint arXiv:0801.0007},
year = {2014}
}
Comments
We wrote a more detailed introduction. 13 pages, 8 figures