Journal of K-theory: K-theory and its Applications to Algebra, Geometry, and Topology

Research Article

Finitely summable Fredholm modules over higher rank groups and lattices

Michael Puschnigga1

a1 Institut de Mathématiques de Luminy, UMR 6206 du CNRS, Université de la Méditerranée, 163, Avenue de Luminy 13288 Marseille, Cedex 9, France, puschnigg@univmed.fr

Abstract

We give a classification (up to smooth homotopy) of finitely summable Fredholm representations (Fredholm modules) over higher rank groups and lattices. Our results are a direct consequence of work of Bader, Furman, Gelander and Monod on generalizations of Kazhdan's property T for locally compact groups.

(Received June 17 2008)

Key Words

  • Fredholm module;
  • Schatten ideal;
  • bivariant K-theory;
  • Property (T);
  • uniformly convex Banach space;
  • higher rank group;
  • rigidity