Mathematical Research Letters
Volume 21 (2014)
Abstract commensurators of right-angled Artin groups and mapping class groups
Pages: 461 – 467
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.
right-angled Artin group, mapping class group, abstract commensurator
2010 Mathematics Subject Classification
Primary 20E36. Secondary 57M07.