Wieler solenoids, Cuntz–Pimsner algebras and K-theory

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dc.identifier.uri http://dx.doi.org/10.15488/2367
dc.identifier.uri http://www.repo.uni-hannover.de/handle/123456789/2393
dc.contributor.author Deeley, Robin J.
dc.contributor.author Goffeng, Magnus
dc.contributor.author Mesland, Bram
dc.contributor.author Whittaker, Michael F.
dc.date.accessioned 2017-11-17T12:26:22Z
dc.date.available 2019-05-03T22:05:03Z
dc.date.issued 2018
dc.identifier.citation Deeley, R.J.; Goffeng, M.; Mesland, B.; Whittaker, M.F.: Wieler solenoids, Cuntz–Pimsner algebras and K-theory. In: Ergodic Theory and Dynamical Systems 38 (2018), S. 2942-2988. DOI: https://doi.org/10.1017/etds.2017.10
dc.description.abstract We study irreducible Smale spaces with totally disconnected stable sets and their associated K-theoretic invariants. Such Smale spaces arise as Wieler solenoids, and we restrict to those arising from open surjections. The paper follows three converging tracks: one dynamical, one operator algebraic and one K-theoretic. Using Wieler’s theorem, we characterize the unstable set of a finite set of periodic points as a locally trivial fibre bundle with discrete fibres over a compact space. This characterization gives us the tools to analyse an explicit groupoid Morita equivalence between the groupoids of Deaconu–Renault and Putnam–Spielberg, extending results of Thomsen. The Deaconu–Renault groupoid and the explicit Morita equivalence lead to a Cuntz–Pimsner model for the stable Ruelle algebra. The K-theoretic invariants of Cuntz–Pimsner algebras are then studied using the Cuntz–Pimsner extension, for which we construct an unbounded representative. To elucidate the power of these constructions, we characterize the Kubo–Martin–Schwinger (KMS) weights on the stable Ruelle algebra of a Wieler solenoid. We conclude with several examples of Wieler solenoids, their associated algebras and spectral triples. eng
dc.language.iso eng
dc.publisher Cambridge : Cambridge University Press
dc.relation.ispartofseries Ergodic Theory and Dynamical Systems 38 (2018)
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.
dc.subject Cuntz–Pimsner algebra eng
dc.subject K-theory eng
dc.subject Kubo–Martin–Schwinger (KMS) eng
dc.subject.ddc 510 | Mathematik ger
dc.title Wieler solenoids, Cuntz–Pimsner algebras and K-theory
dc.type article
dc.type Text
dc.relation.issn 0143-3857
dc.relation.doi https://doi.org/10.1017/etds.2017.10
dc.bibliographicCitation.volume 38
dc.bibliographicCitation.firstPage 2942
dc.bibliographicCitation.lastPage 2988
dc.description.version publishedVersion
tib.accessRights frei zug�nglich

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