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

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.

8 pages; incorporates referee comments

References in corpus (4)

• Embedability between right-angled Artin groups
• Quasiflats in CAT(0) complexes
• On power subgroups of mapping class groups
• Right-angled Artin groups and Out(F_n) I: quasi-isometric embeddings