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2008 One-point reductions of finite spaces, $h$–regular CW–complexes and collapsibility
Jonathan Barmak, Elias Minian
Algebr. Geom. Topol. 8(3): 1763-1780 (2008). DOI: 10.2140/agt.2008.8.1763

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.

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Jonathan Barmak. Elias Minian. "One-point reductions of finite spaces, $h$–regular CW–complexes and collapsibility." Algebr. Geom. Topol. 8 (3) 1763 - 1780, 2008. https://doi.org/10.2140/agt.2008.8.1763

Information

Received: 12 March 2008; Revised: 5 September 2008; Accepted: 5 September 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1227.55005
MathSciNet: MR2448871
Digital Object Identifier: 10.2140/agt.2008.8.1763

Subjects:
Primary: 55P15, 55U05, 57Q05, 57Q10
Secondary: 06A06, 52B70

Rights: Copyright © 2008 Mathematical Sciences Publishers

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