1993/10/12 by John Meier, Meier, John, Leonard VanWyk +2
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Topology and Set Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.GR
paper · pdf · doi:10.48550/arxiv.math/9310202
Plain Tex, 19 pages, no figures
arxiv created 1993/10/12 · openalex publication_date 1993/10/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a finite simplicial graph \cal G, the graph group G\cal G" is the group with generators in one-to-one correspondence with the vertices of \cal G and with relations stating two generators commute if their associated vertices are adjacent in \cal G. The Bieri-Neumann-Strebel invariant can be explicitly described in terms of the original graph \cal G and hence there is an explicit description of the distribution of finitely generated normal subgroups of G\cal G with abelian quotient. We construct Eilenberg-MacLane spaces for graph groups and find partial extensions of this work to the higher dimensional invariants.