Volume 8, issue 3 (2008)

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

Jonathan Ariel Barmak and Elias Gabriel Minian

Algebraic & Geometric Topology 8 (2008) 1763–1780

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.

finite topological spaces, simplicial complexes, regular CW-complexes, collapses, weak homotopy types, posets
Mathematical Subject Classification 2000
Primary: 55U05, 55P15, 57Q05, 57Q10
Secondary: 06A06, 52B70
Received: 12 March 2008
Revised: 5 September 2008
Accepted: 5 September 2008
Published: 9 October 2008
Jonathan Ariel Barmak
Departamento de Matematica
Universidad de Buenos Aires
Buenos Aires
Elias Gabriel Minian
Departamento de Matematica
Universidad de Buenos Aires
Buenos Aires