Abstract commensurators of right-angled Artin groups and mapping class groups

2013/07/31 by Matt Clay, Christopher J. Leininger, Clay, Matt +3
Mathematics · #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GR #math.GT #msc:20E36 #msc:57M07

paper · pdf · doi:10.48550/arxiv.1307.8387

8 pages; incorporates referee comments

arxiv created 2014/03/18 · arxiv updated 2014/03/19

Abstract

We prove that, aside from the obvious exceptions, the mapping class group of a compact orientable surface is not abstractly commensurable with any right-angled Artin group. Our argument applies to various subgroups of the mapping class group---the subgroups generated by powers of Dehn twists and the terms of the Johnson filtration---and additionally to the outer automorphism group of a free group and to certain linear groups.

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