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

Document Type


Publication Date



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.


Principal Investigator: Matthew Day

Acknowledgements: The authors would like to thank Dawid Kielak, Lance Miller, Adam Piggott, Henry Schenck, Alex Suciu, and Uli Walther for helpful conversations. They would also like to thank an anonymous referee for comments that improved the paper. Matthew Day was supported in part by NSF grant DMS1206981.