On virtual indicability and property (T) for outer automorphism groups of RAAGs

2020/11/06 by Sale, Andrew · 1 citation
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2011.03576

Abstract

We give a condition on the defining graph of a right-angled Artin group which implies its automorphism group is virtually indicable, that is, it has a finite-index subgroup that admits a homomorphism onto \Z. We use this as part of a criterion that determines precisely when the outer automorphism group of a right-angled Artin group defined on a graph with no separating intersection of links has property (T). As a consequence we also obtain a similar criterion for graphs in which each equivalence class under the domination relation of Servatius generates an abelian group.

Cited by

• On the ℓ²-Betti numbers and algebraic fibring of the (outer) automorphism group of a right-angled Artin group

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