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Type II non-commutative geometry. I. Dixmier trace in von Neumann algebras
Abstract We define the notion of Connes–von Neumann spectral triple and consider the associated index problem. We compute the analytic Chern–Connes character of such a generalized spectral triple andExpand
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TRIANGULATIONS AND THE STABILITY THEOREM FOR FOLIATIONS
Let (M;F) be a smooth foliated manifold. We prove that there exists a triangulation of M such that each simplex is a distinguished chart for the foliation. This result enables us to give a completeExpand
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Index, eta and rho invariants on foliated bundles Dedicated to Jean-Michel Bismut on the occasion of his sixtieth birthday.
We study primary and secondary invariants of leafwise Dirac operators on foliated bundles. Given such an operator, we begin by considering the associated regular self-adjoint operator $D_m$ on theExpand
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Homology of complete symbols and noncommutative geometry
We identify the periodic cyclic homology of the algebra of complete symbols on a differential groupoidGin terms of the cohomology ofS* (G), the cosphere bundle ofA(G), whereA(G)is the Lie algebroidExpand
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La signature basique est un invariant dʼhomotopie feuilletée
Resume Nous montrons que la signature basique dʼun feuilletage riemannien, homologiquement orientable de codimension paire, est un invariant dʼhomotopie feuilletee.
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Index theory for quasi-crystals I. Computation of the gap-label group
Abstract In this paper, we give a complete solution to the gap labelling conjecture for quasi-crystals. The method adopted relies on the index theory for laminations, and the main tools are theExpand
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Gap-labelling for quasi-crystals (proving a conjecture by J. Bellissard)
In the present paper, we give a proof of the gap-labelling conjecture for quasi-crystals. The main tools are the measured index theorem for laminations and a naturality of the longitudinal ChernExpand
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Calcul du label des gaps pour les quasi-cristaux
We give in the present Note a proof of the Bellissard gap-labelling conjecture for quasi-crystals. Our main tools are the measured index theorem for laminations on the one hand, and the naturality ofExpand
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Cyclic cohomology and the family Lefschetz theorem
Abstract. Any closed current on the base of a compact fibration gives rise to a cyclic cocycle on the smooth convolution algebra. We prove that such cocycle furnishes additive maps from theExpand
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