Seminar Algebra and Geometry: Anne Lonjou (Universität Basel)

Actions of Cremona groups on CAT(0) cube complexes.

A key tool to study the plane Cremona group is its action on a hyperbolic space. Saddly, in higher rank such an action is not available. Recently in geometric group theory, actions on CAT(0) cube complexes turned out to be a powerfull tool to study a large class of groups.    

In this talk, based on a common work with Christian Urech, we will construct such complexes on which Cremona groups of rank n act. We will then see which kind of results on these groups we can obtain.

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