Local index formula and twisted spectral triples

Abstract

We prove a local index formula for a class of twisted spectral triples of type III modeled on the transverse geometry of conformal foliations with locally constant transverse conformal factor. Compared with the earlier proof of the untwisted case, the novel aspect resides in the fact that the twisted analogues of the JLO entire cocycle and of its retraction are no longer cocycles in their respective Connes bicomplexes. We show however that the passage to the infinite temperature limit, respectively the integration along the full temperature range against the Haar measure of the positive half-line, has the remarkable effect of curing in both cases the deviations from the cocycle identity.

41 pages; minor changes; To appear in: CMI Proceedings of Noncommutative Geometry Conference in honor of Alain CONNES' 60th birthday

References in corpus (3)

• Hopf algebras, cyclic cohomology and the transverse index theory
• Type III and spectral triples
• An equivariant noncommutative residue

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