Dixmier traces on noncompact isospectral deformations

Abstract

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 $R^l$. 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 $R^l$, under mild restrictions on the geometry of the manifold which guarantee the Dixmier traceability of those operators.

30 pages, no figures; several minor improvements, to appear in J. Funct. Anal

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Cited by in corpus (2)

• Position-dependent noncommutative products: classical construction and field theory
• Notes on "quantum gravity" and non-commutative geometry