A contractible complex generalizing the McCullough-Miller space is constructed for pure symmetric automorphism groups of right-angled Artin groups, with applications to cohomological dimension and l2-cohomology.
Embedding problem between right-angled Artin groups
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abstract
Given a graph $\Gamma$, the right-angled Artin group $A(\Gamma)$ is given by the presentation $\langle u \in V(\Gamma) \mid [u,v]=1, \ \{u,v\} \in E(\Gamma) \rangle$. The Embedding Problem in right-angled Artin groups asks, given two finite graphs $\Phi,\Psi$, how to determine whether or not $A(\Phi)$ is isomorphic to a subgroup of $A(\Psi)$. These are the notes of a mini-course given at the CIRM in April 2022, dedicated to a geometric point of view on this embedding problem, based on quasi-median graphs.
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The McCullough-Miller complex for right angled Artin groups
A contractible complex generalizing the McCullough-Miller space is constructed for pure symmetric automorphism groups of right-angled Artin groups, with applications to cohomological dimension and l2-cohomology.