Local Cyclic Cohomology of Group Banach Algebras and the bivariant Chern-Connes Character of the Gamma-Element, by Michael Puschnigg

We compute the local cyclic cohomology of the group Banach algebra of fundamental groups of compact manifolds of nonpositive curvature.

This is essentially the first calculation of local cyclic cohomology by means of resolutions and the explicit definition of the local cyclic complex. We use this calculation to determine the image of Kasparov's gamma element under the bivariant Chern-Connes character in bivariant local cyclic cohomology for groups satisfying in addition the property of rapid decay.

Michael Puschnigg <puschni@math.uni-muenster.de>