Cyclic Cohomology and Higher Rank Lattices

We review topologically Nistor’s computation of the homogeneous part of the periodic cyclic cohomology of crossed products Γ⋉A of torsion-free discrete groups Γ with a complex Γ-algebra A. We use periodic cyclic cohomology associated to bornological algebras. Let G be a complex connected semisimple Lie group and B be a minimal parabolic subgroup of G. Applied to torsion-free discrete subgroups Γ of G and the algebra A of smooth functions on the Furstenberg boundary G/B, the construction yields under a weak topological condition, together with the classical splitting principle, the surjectivity of the map HP `