Tuesday, 2 August, 14:45-15:45, Room 4102


Chris Hruska (University of Wisconsin Milwaukee)


How to Cubulate Groups


(Joint with Dani Wise)

If a group G acts on a CAT(0) cube complex, the action induces a very
rich structure on the group. Sageev showed that actions on CAT(0) cube
complexes correspond to "codimension-1" subgroups, which coarsely
separate the group into two complementary components. We think of
these components as "halfspaces" and the cutting subgroup as a "wall".

Some groups admit codimension-1 subgroups, and some don't. Indeed the
existence of actions on cube complexes is closely related to
representation theoretic notions such as Kazhdan's Property (T) and
its strong negation, a-T-menability.

I will discuss "cubulations" of groups: how to construct them and how
to recognize some of their basic finiteness properties.

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