2008/05/31 by Jee Hyoun Kim, Ki Hyoung Ko, Hyo Won Park · 1 citation
Mathematics · #math.GT #math.GR #msc:20F36 #msc:20F65 #msc:57M15
published as Trans. Amer. Math. Soc. (2010) · 52 pages, 30 figures
arxiv created 2010/06/13 · arxiv updated 2010/06/24
We give a necessary and sufficient condition for a graph to have a right-angled Artin group as its braid group for braid index ≥ 5. In order to have the necessity part, graphs are organized into small classes so that one of homological or cohomological characteristics of right-angled Artin groups can be applied. Finally we show that a given graph is planar iff the first homology of its 2-braid group is torsion-free and leave the corresponding statement for n-braid groups as a conjecture along with few other conjectures about graphs whose braid groups of index ≤ 4 are right-angled Artin groups.