2008/01/04 by Jonathan Ariel Barmak, Jonathan Barmak, Elias Gabriel Minian +1
Computer Science · Mathematics · #Algebra over a field #Digital Image Processing Techniques #Finite set #Homotopy #Homotopy and Cohomology in Algebraic Topology #Reduction (mathematics) #Topological and Geometric Data Analysis #Topology (electrical circuits) #math.AT #math.CO #math.GT #msc:06A06 #msc:52B70 #msc:55P15 #msc:55U05 #msc:57Q05 #msc:57Q10 #sort
paper · pdf · doi:10.2140/agt.2008.8.1763
published as Algebr. Geom. Topol. 8 (2008) 1763-1780 · We wrote a more detailed introduction. 13 pages, 8 figures
arxiv created 2008/01/04 · openalex publication_date 2008/10/09 · arxiv updated 2014/09/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.