Guillaume Dumas, University of Maryland
Boundedness of weak quasi-cocycles for higher rank simple groups
If G is a second countable locally compact group, the Delorme-Guichardet theorem states that Kazhdan property (T) is equivalent to the fixed-point property for continuous affine isometric actions on Hilbert spaces—that is, every 1-cocycle with values in a Hilbert space is bounded. Many rigidity statements rely on property (T): for example, morphisms of G into R are trivial. However, it does not provide tools for studying quasi-homomorphisms, since these maps do not respect the group structure. In order to study this class of maps, Ozawa introduced wq-cocycles, which respect a cocycle identity up to a bounded error. A group is said to have property (TTT) if all wq-cocycles are bounded. In this talk, I will discuss the relationship between this property and other more analytical forms of “almost” property (T). I will also explain how to prove that a group possesses this property, with a focus on simple groups and their lattices.
QNC 1507 or Join on Zoom