JournalsjncgVol. 8, No. 1pp. 1–43

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

  • Adam Rennie

    Australian National University, Canberra
  • Roger Senior

    Australian National University, Canberra
The resolvent cocycle in twisted cyclic cohomology and a local index formula for the Podleś  sphere cover

Abstract

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.

Cite this article

Adam Rennie, Roger Senior, The resolvent cocycle in twisted cyclic cohomology and a local index formula for the Podleś sphere. J. Noncommut. Geom. 8 (2014), no. 1, pp. 1–43

DOI 10.4171/JNCG/147