Journal of Noncommutative Geometry


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Volume 8, Issue 1, 2014, pp. 1–43
DOI: 10.4171/JNCG/147

Published online: 2014-03-20

The resolvent cocycle in twisted cyclic cohomology and a local index formula for the Podleś sphere

Adam Rennie[1] and Roger Senior[2]

(1) Australian National University, Canberra
(2) Australian National University, Canberra

We continue the investigation of twisted homology theories in the context of dimension drop phenomena. This work unifies previous equivariant index calculations in twisted cyclic cohomology. We do this by proving the existence of the resolvent cocycle, a finitely summable analogue of the JLO cocycle, under weaker smoothness hypotheses and in the more general setting of ‘modular’ spectral triples. As an application we show that using our twisted resolvent cocycle, we can obtain a local index formula for the Podleś sphere. The resulting twisted cyclic cocycle has non-vanishing Hochschild class which is in dimension 2.

Keywords: Spectral triple, cyclic cohomology, Kasparov theory, q-deformations, Podleś sphere

Rennie Adam, Senior Roger: The resolvent cocycle in twisted cyclic cohomology and a local index formula for the Podleś sphere. J. Noncommut. Geom. 8 (2014), 1-43. doi: 10.4171/JNCG/147