Coarse cubical rigidity

Abstract: When a group $G$ admits nice actions on $\mathrm{CAT}(0)$ cube complexes, understanding the space of all such actions can provide useful information on the outer automorphism group $\mathrm{Out}(G)$. As a classical example, the Culler-Vogtmann outer space is (roughly) the space of all geometric actions of the free group $F_n$ on a $1$-dimensional cube complex (a tree). In general, however, spaces of cubulations tend to be awkwardly vast, even for otherwise rigid groups such as the hexagon RAAG. In an attempt to tame these spaces, we show that all cubulations of many right-angled Artin and Coxeter groups coarsely look the same, in a strong sense: they all induce the same coarse median structure on the group.

This is joint work with Ivan Levcovitz and Michah Sageev.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( paper )

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Geometry and topology online

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The talks start at 13:30. Talks are typically fifty minutes long, with ten minutes for questions.

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