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Dixmier traces on noncompact isospectral deformations

Victor Gayral·Bruno Iochum·Joseph C. Varilly
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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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Victor Gayral, Bruno Iochum, Joseph C. Varilly. 2006-04-06. Dixmier traces on noncompact isospectral deformations. https://arxiv.org/abs/hep-th/0507206

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