Ponente: Damien Gaboriau
Institución: École Normale Supérieure de Lyon, Francia
29/01/2019 de 12:00 a 13:00
Dónde Auditorio "Alfonso Nápoles Gándara"
Few results are know about the L2-Betti numbers of Aut(Fn) and Out(Fn), the groups of automorphisms (resp. outer automorphisms) of the free group Fn. Their virtual geometric dimension (smallest dimension of a K(G,1) for torsion-free finite index subgroups) are 2n−2, resp. 2n−3. I shall show that the top-dimensional L2-Betti numbers of Aut(Fn) and Out(Fn) do not vanish.
By Lück approximation theorem, this implies that these groups admit finite index subgroups with non-vanishing top-dimensional rational cohomology; in fact the usual Betti numbers for finite index subgroups grow linearly with the index.
I will review the basics of the theory and stay at an elementary level.