Geodesic
One-point reductions of finite spaces, h–regular CW–complexes and collapsibility
Barmak, Jonathan1 ; Minian, Elias1
1Departamento de Matematica, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina
Algebraic and Geometric Topology, Tome 8 (2008) no. 3, pp. 1763-1780
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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 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.

DOI : 10.2140/agt.2008.8.1763
Keywords: finite topological spaces, simplicial complexes, regular CW-complexes, collapses, weak homotopy types, posets

Barmak, Jonathan  1   ; Minian, Elias  1

1 Departamento de Matematica, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina 
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Barmak, Jonathan; Minian, Elias. One-point reductions of finite spaces, h–regular CW–complexes and collapsibility. Algebraic and Geometric Topology, Tome 8 (2008) no. 3, pp. 1763-1780. doi: 10.2140/agt.2008.8.1763

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