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- W2616998334 abstract "We prove that if a right-angled Artin group $A_Gamma$ is abstractly commensurable to a group splitting non-trivially as an amalgam or HNN-extension over $mathbb{Z}^n$, then $A_Gamma$ must itself split non-trivially over $mathbb{Z}^k$ for some $kle n$. Consequently, if two right-angled Artin groups $A_Gamma$ and $A_Delta$ are commensurable and $Gamma$ has no separating $k$-cliques for any $kle n$ then neither does $Delta$, so smallest size of separating clique is a commensurability invariant. We also discuss some implications for issues of quasi-isometry. Using similar methods we also prove that for $nge 4$ the braid group $B_n$ is not abstractly commensurable to any group that splits non-trivially over a free group-free subgroup, and the same holds for $nge 3$ for the loop braid group $LB_n$. Our approach makes heavy use of the Bieri--Neumann--Strebel invariant." @default.
- W2616998334 created "2017-06-05" @default.
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- W2616998334 date "2019-05-21" @default.
- W2616998334 modified "2023-09-26" @default.
- W2616998334 title "Commensurability invariance for abelian splittings of right-angled Artin groups, braid groups and loop braid groups" @default.
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- W2616998334 doi "https://doi.org/10.2140/agt.2019.19.1247" @default.
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