2009/09/25 by Jon McCammond, McCammond, Jon
Computer Science · Mathematics · #20F05 #20F36 #20F65 #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.GR #msc:20F05 #msc:20F36 #msc:20F65
paper · pdf · doi:10.48550/arxiv.0909.4774
18 pages, 7 figures
arxiv created 2009/09/25 · openalex publication_date 2009/09/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Group presentations are implicit descriptions of 2-dimensional cell complexes with only one vertex. While such complexes are usually sufficient for topological investigations of groups, multi-vertex complexes are often preferable when the focus shifts to geometric considerations. In this article, I show how to quickly describe the most important multi-vertex 2-complexes using a slight variation of the traditional group presentation. As an illustration I describe multi-vertex 2-complexes for torus knot groups and one-relator Artin groups from which their elementary properties are easily derived. The latter are used to give an easy geometric proof of a classic result of Appel and Schupp.