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Wieler solenoids, C...
Wieler solenoids, Cuntz–Pimsner algebras and K-theory
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- DEELEY, ROBIN J. (författare)
- University of Hawaii
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- Goffeng, Magnus C H T, 1987 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg
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- MESLAND, BRAM (författare)
- University of Hanover, Germany
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- WHITTAKER, MICHAEL F. (författare)
- University of Glasgow
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(creator_code:org_t)
- 2017-05-02
- 2018
- Engelska.
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Ingår i: Ergodic Theory and Dynamical Systems. - : Cambridge University Press (CUP). - 0143-3857 .- 1469-4417. ; 38:8, s. 2942-2988
- Relaterad länk:
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https://gup.ub.gu.se...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- © Cambridge University Press, 2017 We study irreducible Smale spaces with totally disconnected stable sets and their associated (Formula presented.)-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 (Formula presented.)-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 (Formula presented.)-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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
- NATURVETENSKAP -- Matematik -- Geometri (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Geometry (hsv//eng)
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