Hodge theory for group cohomology and local rigidity
David Fisher (University of Indiana)
Abstract:
I will discuss a far ranging generalization of (one aspect of)
property (T): the relation between vanishing of cohomology
and vanishing of reduced cohomology. The generalization
applies to cohomology in all degrees and to a wide variety
of classes of representations. The main ingredient is a form
of Hodge theory for group cohomology. I will also discuss
applications to local rigidity and if time permits to cohomology
of lattices in Lie groups.