On von Neumann spectral triples

Abstract

We define the notion of von Neumann spectral triple and consider the associated index problem. We compute the analytic Chern-Connes character of such a von Neumann spectral triple and prove the corresponding local formula for its Hochschild class. This formula involves the Dixmier trace for $I{I}_{\infty }$ von Neumann algebras. In the case of foliations, we identify this Dixmier trace with the corresponding measured Wodzicki residue.

This paper has been withdrawn by the authors

References in corpus (3)

• Hopf algebras, cyclic cohomology and the transverse index theory
• Noncommutative Riemann integration and and Novikov-Shubin invariants for open manifolds
• Foliated group actions and cyclic cohomology

Cited by in corpus (3)

• Dimensions and singular traces for spectral triples, with applications to fractals
• Modular Theory, Non-Commutative Geometry and Quantum Gravity
• A walk in the noncommutative garden