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2018 Smale spaces from self-similar graph actions
Inhyeop Yi
Rocky Mountain J. Math. 48(4): 1359-1384 (2018). DOI: 10.1216/RMJ-2018-48-4-1359

Abstract

We show that, for contracting and regular self-similar graph actions, the shift maps on limit spaces are positively expansive local homeomorphisms. From this, we find that limit solenoids of contracting and regular self-similar graph actions are Smale spaces and that the unstable Ruelle algebras of the limit solenoids are strongly Morita equivalent to the Cuntz-Pimsner algebras by Exel and Pardo if self-similar graph actions satisfy the contracting, regular, pseudo free and $G$-transitive conditions.

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Inhyeop Yi. "Smale spaces from self-similar graph actions." Rocky Mountain J. Math. 48 (4) 1359 - 1384, 2018. https://doi.org/10.1216/RMJ-2018-48-4-1359

Information

Published: 2018
First available in Project Euclid: 30 September 2018

zbMATH: 06958783
MathSciNet: MR3859762
Digital Object Identifier: 10.1216/RMJ-2018-48-4-1359

Subjects:
Primary: 37D20, 46L05, 46L55

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 4 • 2018
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