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Coloquio del IMUNAM - C.U.

Martes 29 de enero de 2019. 12:00 horas.
Auditorio "Alfonso Nápoles Gándara". IMUNAM - C.U.

Enero 2019 | Auditorio "Alfonso Nápoles Gándara" |  12:00 horas

 Martes 29 enero

 On the non-vanishing of the cohomology of Aut(Fn) and Out(Fn) in top dimensions

Damien Gaboriau, École Normale Supérieure de Lyon, Francia


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 FnTheir virtual geometric dimension (smallest dimension of a K(G,1) for torsion-free finite index subgroups) are 2n2, resp. 2n3I 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.

  • Coloquio del IMUNAM - C.U.

    Coloquio del IMUNAM - C.U.

    Auditorio "Alfonso Nápoles Gándara"