2010/08/07 by Iain R. Aitchison, Aitchison, Iain R.
Computer Science · Mathematics · #2010 MSC. Primary: 57M05 #20F65 #30F40 #57M50 #57N10 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Secondary: 20F05 #math.GR #math.GT #msc:2010 #msc:20F05 #msc:20F65 #msc:30F40 #msc:57M05 #msc:57M50 #msc:57N10 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1008.1311
18 pages, 4 figures
arxiv created 2010/08/07 · openalex publication_date 2010/08/07 · arxiv updated 2010/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that every finitely presentable group G arises as the fundamental group of an orientable 3-complex obtained from a hyperbolic link complement, by coning each boundary torus of the link exterior to a distinct point. We define the closed-link-genus, clg(G), of any finitely presentable group G, which completely characterizes fundamental groups of closed orientable 3-manifolds: clg(G)=0 if and only if G is the fundamental group of a closed orientable 3-manifold. Moreover clg(G) gives an upper bound for the concept `genus(G)' of genus defined earlier by Aitchison and Reeves, and in turn is bounded by the minimal number of relations among all finite presentations of G.