Barthelme, Thomas and Mann, Kathryn and Bowden, Jonathan (2024) Orbit equivalences of R-covered Anosov flows and hyperbolic-like actions on the line. GEOMETRY & TOPOLOGY, 28 (2). pp. 867-899. ISSN 1465-3060, 1364-0380
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We prove a rigidity result for group actions on the line whose elements have what we call "hyperboliclike" dynamics. Using this, we give a rigidity theorem for R-covered Anosov flows on 3-manifolds, characterizing orbit equivalent flows in terms of the elements of the fundamental group represented by periodic orbits. As consequences of this, we give an efficient criterion to determine the isotopy classes of self-orbit equivalences of R-covered Anosov flows, and prove finiteness of contact Anosov flows on any given manifold. In the appendix, with Jonathan Bowden, we prove that orbit equivalences of contact Anosov flows correspond exactly to isomorphisms of the associated contact structures. This gives a powerful tool to translate results on Anosov flows to contact geometry and vice versa. We illustrate its use by giving two new results in contact geometry: the existence of manifolds with arbitrarily many distinct Anosov contact structures, answering a question of Foulon, Hasselblatt and Vaugon, and a virtual description of the group of contact transformations of a Anosov contact structure, generalizing a result of Giroux and Massot.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CONVERGENCE GROUPS; HOMOLOGY; BUNDLES |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 03 Dec 2025 07:30 |
| Last Modified: | 03 Dec 2025 07:30 |
| URI: | https://pred.uni-regensburg.de/id/eprint/64480 |
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