Infinitesimal rigidity of boundary lattice actions

Abstract

In Part 1 we describe a duality method for calculating twisted cocycles. In Part 2 we use our method to prove various results on cohomological rigidity of higher-rank cocompact lattice actions. In Part 3 we use the results of Parts 1 and 2 to prove infinitesimal rigidity of the actions of cocompact lattices on the maximal boundaries of some non-compact type symmetric spaces.