Actions of Cremona groups on CAT(0) cube complexes

Abstract: A key tool to study the plane Cremona group is its action on a hyperbolic space. Sadly, 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 powerful 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. Then, we will see which kind of results on these groups we can obtain.

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".