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One-point reductions of
finite spaces, $h$–regular CW–complexes and
collapsibility
Jonathan Ariel Barmak and Elias Gabriel Minian |
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Algebraic & Geometric Topology 8 (2008) 1763–1780
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Abstract |
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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 –regular CW–complex, generalizing the concept of regular CW–complex, and prove that the –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
finite topological spaces, simplicial complexes, regular
CW-complexes, collapses, weak homotopy types, posets
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Mathematical Subject Classification 2000
Primary: 55U05, 55P15, 57Q05, 57Q10
Secondary: 06A06, 52B70
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References |
Publication
Received: 12 March 2008
Revised: 5 September 2008
Accepted: 5 September 2008
Published: 9 October 2008
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Authors |
| Jonathan Ariel Barmak | |
| Departamento de Matematica FCEyN Universidad de Buenos Aires Buenos Aires Argentina |
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| http://mate.dm.uba.ar/~jbarmak/ | |
| Elias Gabriel Minian | |
| Departamento de Matematica FCEyN Universidad de Buenos Aires Buenos Aires Argentina |
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| http://mate.dm.uba.ar/~gminian/ | |
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