Subspace arrangements, BNS invariants, and pure symmetric outer automorphisms of right-angled Artin groups
Right-angled Artin groups, partially commutative groups, outer automorphism groups, BNS invariants, Bieri–Neumann–Strebel invariants, subspace arrangements, homology theory
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.
Day, Matthew B. and Wade, Richard, "Subspace arrangements, BNS invariants, and pure symmetric outer automorphisms of right-angled Artin groups" (2018). Mathematical Sciences Faculty Publications and Presentations. 3.