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Type II non-commutative geometry. I. Dixmier trace in von Neumann algebras

- Moulay-Tahar Benameur, T. Fack
- Mathematics
- 15 January 2006

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 and… Expand

73 5- PDF

TRIANGULATIONS AND THE STABILITY THEOREM FOR FOLIATIONS

- Moulay-Tahar Benameur
- Mathematics
- 1 June 1997

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 complete… Expand

13 2- PDF

Index, eta and rho invariants on foliated bundles Dedicated to Jean-Michel Bismut on the occasion of his sixtieth birthday.

- Moulay-Tahar Benameur, Paolo Piazza
- Mathematics
- 12 September 2008

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 the… Expand

25 1- PDF

Homology of complete symbols and noncommutative geometry

- Moulay-Tahar Benameur, V. Nistor
- Mathematics
- 16 August 2000

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 algebroid… Expand

15 1- PDF

La signature basique est un invariant dʼhomotopie feuilletée

- Moulay-Tahar Benameur, Alexandre Rey-Alcantara
- Mathematics
- 1 July 2011

Resume Nous montrons que la signature basique dʼun feuilletage riemannien, homologiquement orientable de codimension paire, est un invariant dʼhomotopie feuilletee.

2 1

Index theory for quasi-crystals I. Computation of the gap-label group

- Moulay-Tahar Benameur, H. Oyono-Oyono
- Mathematics
- 1 November 2007

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 the… Expand

18 1

Gap-labelling for quasi-crystals (proving a conjecture by J. Bellissard)

- Moulay-Tahar Benameur, H. Oyono-Oyono
- Mathematics, Physics
- 12 December 2001

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 Chern… Expand

19 1- PDF

Calcul du label des gaps pour les quasi-cristaux

- Moulay-Tahar Benameur, Hervé Oyono-Oyono
- Mathematics
- 2002

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 of… Expand

9 1

NONCOMMUTATIVE GEOMETRY AND ABSTRACT INTEGRATION THEORY

- Moulay-Tahar Benameur
- Mathematics
- 1 March 2003

7 1

Cyclic cohomology and the family Lefschetz theorem

- Moulay-Tahar Benameur
- Mathematics
- 1 May 2002

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 the… Expand

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