2009/02/05 by Henri Moscovici, Moscovici, Henri · 2 citations
Mathematics · Physics and Astronomy · #46L80 #58B34 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Black Holes and Theoretical Physics #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #math.KT #math.OA #msc:46L80 #msc:58B34
paper · pdf · doi:10.48550/arxiv.0902.0835
41 pages; minor changes; To appear in: CMI Proceedings of Noncommutative Geometry Conference in honor of Alain CONNES' 60th birthday
openalex publication_date 2009/02/05 · arxiv created 2009/09/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.