Factorisation of equivariant spectral triples in unbounded KK-theory

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dc.identifier.uri http://dx.doi.org/10.15488/11602
dc.identifier.uri https://www.repo.uni-hannover.de/handle/123456789/11693
dc.contributor.author Forsyth, Iain eng
dc.contributor.author Rennie, Adam eng
dc.date.accessioned 2021-12-21T07:56:26Z
dc.date.available 2021-12-21T07:56:26Z
dc.date.issued 2019
dc.identifier.citation Forsyth, I.; Rennie, A.: Factorisation of equivariant spectral triples in unbounded KK-theory. In: Journal of the Australian Mathematical Society 107 (2019), Nr. 2, S. 145-180. DOI: https://doi.org/10.1017/S1446788718000423 eng
dc.description.abstract We provide sufficient conditions to factorise an equivariant spectral triple as a Kasparov product of unbounded classes constructed from the group action on the algebra and from the fixed point spectral triple. We show that if factorisation occurs, then the equivariant index of the spectral triple vanishes. Our results are for the action of compact abelian Lie groups, and we demonstrate them with examples from manifolds and θ-deformations. In particular, we show that equivariant Dirac-type spectral triples on the total space of a torus principal bundle always factorise. Combining this with our index result yields a special case of the Atiyah–Hirzebruch theorem. We also present an example that shows what goes wrong in the absence of our sufficient conditions (and how we get around it for this example). eng
dc.language.iso eng eng
dc.publisher Cambridge : Cambridge Univ. Press
dc.relation.ispartofseries Journal of the Australian Mathematical Society 107 (2019), Nr. 2 eng
dc.rights Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich. eng
dc.subject KK-theory eng
dc.subject spectral triple eng
dc.subject Kasparov product eng
dc.subject.ddc 510 | Mathematik eng
dc.title Factorisation of equivariant spectral triples in unbounded KK-theory eng
dc.type Article eng
dc.type Text eng
dc.relation.essn 1446-8107
dc.relation.issn 1446-7887
dc.relation.doi 10.1017/S1446788718000423
dc.description.version publishedVersion eng
tib.accessRights frei zug�nglich eng

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