1-cohomology of groups acting on trees and cocycle growth (Thibaut Dumont, University of Jyväskylä)

19.12.2017 10:30

In this talk, I will discuss some aspects of representation theory of groups acting on trees. I will briefly recall the well-known correspondence between 1-cohomology and affine isometric actions on Hilbert spaces, as well as important related properties such as Kazhdan's property (T) and Haagerup's property also known as a-T-menability. The unifying theme here is the norm growth of 1-cocycles. When a group acts on a tree, the Busemann 1-cocycle provides an interesting cohomology class for the group. The norm of the former may be bounded above using explicit tools such as the Poisson transform introduced by B. Klingler. Independently, P.-N. Jolissaint and A. Gournay obtained a sharper result for harmonic 1-cocycles. If times permit, I will discuss high-rank generalizations.

Lieu

Room 623, Séminaire "Groupes et Géométrie"

entrée libre