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

Matt Clay; Christopher J. Leininger; Dan Margalit

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arXiv · 1307.8387

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

Matt Clay·Christopher J. Leininger·Dan Margalit

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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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Matt Clay, Christopher J. Leininger, Dan Margalit. 2014-03-18. Abstract commensurators of right-angled Artin groups and mapping class groups. https://arxiv.org/abs/1307.8387

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