The Bieri-Neumann-Strebel Invariant of the Pure Symmetric Automorphisms of a Right-Angled Artin Group

We compute the BNS-invariant for the pure symmetric automorphism groups of right-angled Artin groups. We use this calculation to show that the pure symmetric automorphism group of a right-angled Artin group is itself not a right-angled Artin group provided that its defining graph contains a separating intersection of links

RAAGs in Ham

We prove that every RAAG (a Right-Angled Artin Group) embeds in the group of Hamiltonian symplectomorphisms of the 2-sphere.Comment: 23 pages, 2 figure

An obstruction to embedding right-angled Artin groups in mapping class groups

For every orientable surface of finite negative Euler characteristic, we find a right-angled Artin group of cohomological dimension two which does not embed into the associated mapping class group. For a right-angled Artin group on a graph \gam to embed into the mapping class group of a surface $S$, we show that the chromatic number of \gam cannot exceed the chromatic number of the clique graph of the curve graph $\mathcal{C}(S)$. Thus, the chromatic number of \gam is a global obstruction to embedding the right-angled Artin group A(\gam) into the mapping class group \Mod(S).Comment: Added more details to the proof of Lemma 3.3. To appear in IMR

Homological stability for automorphism groups of RAAGs

We show that the homology of the automorphism group of a right-angled Artin group stabilizes under taking products with any right-angled Artin group.Comment: final versio