Groups and Dynamics Seminar

Date: March 10, 2021

Time: 12:00PM - 1:00PM

Location: BLOC 220

Speaker: Damien Gaboriau, École Normale Supérieure de Lyon

Title: On dense totipotent free subgroups in full groups

Abstract: I will present the following notions and results. The perfect kernel of a countable group Gamma is the largest closed subspace of the space of subgroups of Gamma without isolated points. We introduce the class of totipotent ergodic probability measure preserving (p.m.p.) actions of Gamma: those for which almost every point-stabilizer has dense conjugacy class in the perfect kernel. Equivalently, the support of the associated Invariant Random Subgroup (IRS) coinicdes with the whole perfect kernel (it is as large as possible). We prove that every ergodic p.m.p. equivalence relation R of cost