A Homotopy Theory for Graphs

2004/03/09 by Eric Babson, E. Babson, Hélène Barcelo +9 · 5 citations
Computer Science · Mathematics · #05C99(Primary) #55Q99 (Secondary) #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.CO #msc:55Q99

paper · pdf · doi:10.48550/arxiv.math/0403146

11 pages, 3 figures

arxiv created 2004/03/09 · openalex publication_date 2004/03/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The recently introduced A-homotopy groups for graphs are investigated. The main concern of the present article is the construction of an infinite cell complex, the homotopy groups of which are isomorphic to the A-homotopy groups of the given graph. We present a natural candidate for such a cell complex, together with a homomorphism between the corresponding groups that indeed yields an isomorphism, if a cubical analog of the simplicial approximation theorem holds, which - so far - we were unable to prove.

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