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

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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Keywords

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

References

Publication

Received: 12 March 2008

Revised: 5 September 2008

Accepted: 5 September 2008

Published: 9 October 2008

Authors

Jonathan Ariel Barmak
Departamento de Matematica FCEyN Universidad de Buenos Aires Buenos Aires Argentina
http://mate.dm.uba.ar/~jbarmak/
Elias Gabriel Minian
Departamento de Matematica FCEyN Universidad de Buenos Aires Buenos Aires Argentina
http://mate.dm.uba.ar/~gminian/

Volume 8, issue 3 (2008)

Jonathan Ariel Barmak and Elias Gabriel Minian

Abstract