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The resolvent cocycle in twisted cyclic cohomology and a local index formula for the Podle´s sphere

Journal Article


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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 Podles sphere. The resulting twisted cyclic cocycle has non-vanishing Hochschild class which is in dimension 2.

Publication Date


  • 2014

Citation


  • Rennie, A. & Senior, R. (2014). The resolvent cocycle in twisted cyclic cohomology and a local index formula for the Podle´s sphere. Journal of Noncommutative Geometry, 8 (1), 1-43.

Scopus Eid


  • 2-s2.0-84898736798

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3523&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2514

Number Of Pages


  • 42

Start Page


  • 1

End Page


  • 43

Volume


  • 8

Issue


  • 1

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 Podles sphere. The resulting twisted cyclic cocycle has non-vanishing Hochschild class which is in dimension 2.

Publication Date


  • 2014

Citation


  • Rennie, A. & Senior, R. (2014). The resolvent cocycle in twisted cyclic cohomology and a local index formula for the Podle´s sphere. Journal of Noncommutative Geometry, 8 (1), 1-43.

Scopus Eid


  • 2-s2.0-84898736798

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3523&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2514

Number Of Pages


  • 42

Start Page


  • 1

End Page


  • 43

Volume


  • 8

Issue


  • 1