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June 2019 Two applications of strong hyperbolicity
Bogdan Nica
Kyoto J. Math. 59(2): 357-366 (June 2019). DOI: 10.1215/21562261-2019-0002

Abstract

We present two analytic applications of the fact that a hyperbolic group can be endowed with a strongly hyperbolic metric. The first application concerns the crossed product C-algebra defined by the action of a hyperbolic group on its boundary. We construct a natural time flow, involving the Busemann cocycle on the boundary. This flow has a natural KMS state, coming from the Hausdorff measure on the boundary, which is furthermore unique when the group is torsion-free. The second application is a short new proof of the fact that a hyperbolic group admits a proper isometric action on an p-space for large enough p.

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Bogdan Nica. "Two applications of strong hyperbolicity." Kyoto J. Math. 59 (2) 357 - 366, June 2019. https://doi.org/10.1215/21562261-2019-0002

Information

Received: 17 November 2016; Revised: 26 February 2017; Accepted: 28 February 2017; Published: June 2019
First available in Project Euclid: 4 February 2019

zbMATH: 07080108
MathSciNet: MR3960297
Digital Object Identifier: 10.1215/21562261-2019-0002

Subjects:
Primary: 20F67

Rights: Copyright © 2019 Kyoto University

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Vol.59 • No. 2 • June 2019
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