14 research outputs found

    Orbifolds are not commutative geometries

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    In this note we show that the crucial orientation condition for commutative geometries fails for the natural spectral triple of an orbifold M/G.Comment: 6 pages, Latex, no figure

    Reconstruction of manifolds in noncommutative geometry

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    We show that the algebra A of a commutative unital spectral triple (A,H,D) satisfying several additional conditions, slightly stronger than those proposed by Connes, is the algebra of smooth functions on a compact spin manifold.Comment: 67 pages, no figures, Latex; major changes, a new Appendix

    Dixmier traces on noncompact isospectral deformations

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    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 RlR^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 RlR^l, under mild restrictions on the geometry of the manifold which guarantee the Dixmier traceability of those operators.Comment: 30 pages, no figures; several minor improvements, to appear in J. Funct. Ana

    Fourier analysis on the affine group, quantization and noncompact Connes geometries

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    We find the Stratonovich-Weyl quantizer for the nonunimodular affine group of the line. A noncommutative product of functions on the half-plane, underlying a noncompact spectral triple in the sense of Connes, is obtained from it. The corresponding Wigner functions reproduce the time-frequency distributions of signal processing. The same construction leads to scalar Fourier transformations on the affine group, simplifying and extending the Fourier transformation proposed by Kirillov.Comment: 37 pages, Latex, uses TikZ package to draw 3 figures. Two new subsections, main results unchange

    Local index formula for SU_q(2)

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    We discuss the local index formula of Connes-Moscovici for the isospectral noncommutative geometry that we have recently constructed on quantum SU(2). We work out the cosphere bundle and the dimension spectrum as well as the local cyclic cocycles yielding the index formula.Comment: 18 pages. v2: minor changes; to appear in K-theor
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