Dixmier traces on noncompact isospectral deformations
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Gayral, Victor
Iochum, Bruno
Várilly Boyle, Joseph C.
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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.
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MATHEMATICS, GEOMETRY
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https://www.sciencedirect.com/science/article/pii/S002212360600067X