Dixmier traces on noncompact isospectral deformations

We extend the isospectral deformations of Connes, Landi and Dubois-Violette to the case of Riemannian spin manifolds carrying a proper action of the noncompact abelian group Rl . Under deformation by a torus action, a standard formula relates Dixmier traces of measurable operators to integrals of functions on the manifold. We show that this relation persists for actions of Rl , under mild restrictions on the geometry of the manifold which guarantee the Dixmier traceability of those operators. © 2006 Elsevier Inc. All rights reserved.