Subspace arrangements, BNS invariants, and pure symmetric outer automorphisms of right-angled Artin groups

Matthew B. Day; Richard D. Wade

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arXiv · 1508.00622

Subspace arrangements, BNS invariants, and pure symmetric outer automorphisms of right-angled Artin groups

Matthew B. Day·Richard D. Wade

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Abstract

We introduce a homology theory for subspace arrangements, and use it to extract a new system of numerical invariants from the Bieri-Neumann-Strebel invariant of a group. We use these to characterize when the set of basis conjugating outer automorphisms (a.k.a. the pure symmetric outer automorphism group) of a right-angled Artin group is itself a right-angled Artin group.

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Matthew B. Day, Richard D. Wade. 2015-08-03. Subspace arrangements, BNS invariants, and pure symmetric outer automorphisms of right-angled Artin groups. https://arxiv.org/abs/1508.00622

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