Outer space for RAAGs

Abstract: In recent years right-angled Artin groups (RAAGs) have assumed a prominent place in geometric group theory and related fields, Now attention is also being focused on their (outer) automorphism groups. The most well-understood examples of outer automorphism groups of RAAGs are $\mathbf{GL}(n,\mathbb{Z})$ and $\mathbf{Out}(F_n)$. $\mathbf{GL}(n,\mathbb{Z})$ can be profitably studied via its action on the symmetric space of marked lattices, and $\mathbf{Out}(F_n)$ via its action on Outer space. We propose an analogous ``outer space'' generalizing both of these, on which the outer automorphism group of an arbitrary RAAG acts properly, and we prove this space is contractible.

This is joint work with Corey Bregman and Ruth Charney.

algebraic geometryalgebraic topologycomplex variablesdifferential geometrygeometric topologymetric geometryquantum algebrarepresentation theory

Audience: researchers in the topic

Sapienza A&G Seminar

Series comments: Weekly research seminar in algebra and geometry.

"Sapienza" Università di Roma, Department of Mathematics "Guido Castelnuovo".