Algebraic & Geometric Topology

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

Jonathan Barmak and Elias Minian

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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.

Article information

Algebr. Geom. Topol., Volume 8, Number 3 (2008), 1763-1780.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55U05: Abstract complexes 55P15: Classification of homotopy type 57Q05: General topology of complexes 57Q10: Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28]
Secondary: 06A06: Partial order, general 52B70: Polyhedral manifolds

finite topological spaces simplicial complexes regular CW-complexes collapses weak homotopy types posets


Barmak, Jonathan; Minian, Elias. One-point reductions of finite spaces, $h$–regular CW–complexes and collapsibility. Algebr. Geom. Topol. 8 (2008), no. 3, 1763--1780. doi:10.2140/agt.2008.8.1763.

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