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Partially hyperbolic
diffeomorphisms homotopic to the identity in dimension $3$,
II: Branching foliations
Thomas Barthelmé, Sérgio R Fenley, Steven Frankel and Rafael Potrie |
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Geometry & Topology 27 (2023) 3095–3181
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Abstract |
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We study –dimensional partially hyperbolic diffeomorphisms that are homotopic to the identity, focusing on the geometry and dynamics of Burago and Ivanov’s center stable and center unstable branching foliations. This extends our previous study of the true foliations that appear in the dynamically coherent case. We complete the classification of such diffeomorphisms in Seifert fibered manifolds. In hyperbolic manifolds, we show that any such diffeomorphism is either dynamically coherent and has a power that is a discretized Anosov flow, or is of a new potential class called a double translation. |
Keywords
partial hyperbolicity, 3–manifolds, foliations
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Mathematical Subject Classification
Primary: 37D30, 57R30, 37C15, 57M50, 37D20
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References |
Publication
Received: 7 August 2020
Revised: 4 February 2022
Accepted: 13 March 2022
Published: 9 November 2023
Proposed: David Gabai
Seconded: Leonid Polterovich, David Fisher
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Authors |
| Thomas Barthelmé | |
| Department of Mathematics and
Statistics Queen’s University Kingston, ON Canada |
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| http://sites.google.com/site/thomasbarthelme | |
| Sérgio R Fenley | |
| Department of Mathematics Florida State University Tallahassee, FL United States |
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| Steven Frankel | |
| Department of Mathematics Washington University in St. Louis St Louis, MO United States |
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| Rafael Potrie | |
| Facultad de Ciencias – Centro de
Matemática Universidad de la República Montevideo Uruguay |
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| http://www.cmat.edu.uy/~rpotrie/ | |
| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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