Year: 2009
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Moscovici, Henri
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1658768125