Explicit cocycles on Furstenberg boundaries (Alessio Savini, Université de Genève)

22.11.2022 10:30

Given a center-free semisimple Lie group without compact factors, it is known that its continuous bounded cohomology can be computed by the complex of essentially bounded functions on the Furstenberg boundary. In order to study the nature of the comparison map, more recently Monod has proved that the complex of (unbounded) measurable functions on the same boundary computes the continuous cohomology, except possibly in some low degrees determined by the rank. We investigate this phenomenon for SL(3,K), with K real of complex, and for products of isometries of hyperbolic spaces and we exhibit an explicit family of cocycles in low degrees. As a consequence we show that the comparison map is an isomorphism in degree 3, which is known for SL(3,K) but new for the product case.
This is a joint work with Michelle Bucher.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Tuesday 22.11.2022, Séminaire "Groupes et géométrie"

entrée libre