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

Matt Clay, Christopher J. Leininger, Dan Margalit

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)461-467
Number of pages7
JournalMathematical Research Letters
Issue number3
StatePublished - 2014
Externally publishedYes


  • Abstract commensurator
  • Mapping class group
  • Right-angled Artin group

ASJC Scopus subject areas

  • General Mathematics


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