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Groups of Anosov-like homeomorphisms and foliations of the plane - lecture 1
Multi angle
Authors : Mann, Kathryn (Author of the conference)
CIRM (Publisher )
37D05 - Hyberbolic orbits and sets
57M60 - Group actions in low dimensions
57S25 - Groups acting on specific manifolds
CIRM (Publisher )
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Abstract :
A theorem of Barbot (building on work of Ghys, Haefliger and others) says that Anosov flows on 3-manifolds are classified up to orbit equivalence by the data of a pair of transverse foliations of the plane and an action of the fundamental group of the 3-manifold. In recent work with T. Barthelmé, as well as C. Bonatti, S. Fenley and S. Frankel, we have been developing an abstract theory of Anosov-like group actions of bifoliated planes, applicable both to the study of flows and as an interesting class of foliation-preserving dynamical systems in its own right. This minicourse will explain some of this theory and the connections between flows and group actions in dimensions 1, 2 and 3.
Keywords : Anosov flow; 3-manifold; groups acting on the plane; hyperbolicity; pseudo-Anosov
MSC Codes : Keywords : Anosov flow; 3-manifold; groups acting on the plane; hyperbolicity; pseudo-Anosov
37D05 - Hyberbolic orbits and sets
57M60 - Group actions in low dimensions
57S25 - Groups acting on specific manifolds
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 10/01/2025 Conference Date : 09/12/2024 Subseries : Research School arXiv category : Dynamical Systems ; Geometric Topology Mathematical Area(s) : Dynamical Systems & ODE ; Topology Format : MP4 (.mp4) - HD Video Time : 01:04:27 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-12-09_Mann_1.mp4 
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Information on the Event
Event Title : Foliations and Diffeomorphism Groups / Feuilletages et Groupes de DifféomorphismeEvent Organizers : Eynard-Bontemps, Hélène ; Meigniez, Gaël ; Nariman, Sam ; Yazdi, Mehdi Dates : 09/12/2024 - 13/12/2024 Event Year : 2024 Event URL : https://conferences.cirm-math.fr/3082.html
Citation Data
DOI : 10.24350/CIRM.V.20275003Cite this video as: Mann, Kathryn (2024). Groups of Anosov-like homeomorphisms and foliations of the plane - lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20275003 URI : http://dx.doi.org/10.24350/CIRM.V.20275003 |
See Also
- [Multi angle] On the group of real-analytic diffeomorphisms - lecture 3 / Author of the conference Takashi, Tsuboi.
- [Multi angle] On the group of real-analytic diffeomorphisms - lecture 2 / Author of the conference Takashi, Tsuboi.
- [Multi angle] On conjugate actions in dimension 1: applications to deformation and distortion - Lecture 3 / Author of the conference Navas, Andrès.
- [Multi angle] On conjugate actions in dimension 1: applications to deformation and distortion - Lecture 2 / Author of the conference Navas, Andrès.
- [Multi angle] Groups of Anosov-like homeomorphisms and foliations of the plane - lecture 3 / Author of the conference Mann, Kathryn.
- [Multi angle] Groups of Anosov-like homeomorphisms and foliations of the plane -Lecture 2 / Author of the conference Mann, Kathryn.
- [Multi angle] Veering triangulations and transverse foliations / Author of the conference Zung, Jonathan.
- [Multi angle] On the group of real-analytic diffeomorphisms - Lecture 1 / Author of the conference Takashi, Tsuboi.
- [Multi angle] Persistently foliar knots / Author of the conference Roberts, Rachel.
- [Multi angle] On conjugate actions in dimension 1: applications to deformation and distortion - Lecture 1 / Author of the conference Navas, Andrès.
- [Multi angle] Using ergodic theory to study the cohomology of diffeomorphism groups / Author of the conference Monod, Nicolas.
- [Multi angle] Dynamics of surface homeomorphisms and fine curve graph / Author of the conference Militon, Emmanuel.
- [Multi angle] Taut foliations through a contact lens / Author of the conference Massoni, Thomas.
- [Multi angle] Torus homeomorphisms and the fine curve graph / Author of the conference Le Roux, Frédéric.
- [Multi angle] Critical regularity and subexponential growth / Author of the conference Kim, Sang-Hyun.
- [Multi angle] Recent progress on groups of area-preserving homeomorphisms / Author of the conference Humilière, Vincent.
- [Multi angle] Distortion elements in groups of interval diffeomorphisms / Author of the conference Eynard-Bontemps, Hélène.
- [Multi angle] Foliations on the plane $ \mathbb{R}^{2}$, pre-laminations on the circle $\mathbb{S}^{1}$, group actions on the circle $\mathbb{S}^{1}$ / Author of the conference Bonatti, Christian.
Bibliography
- BARTHELMÉ, Thomas, FRANKEL, Steven, et MANN, Kathryn. Orbit equivalences of pseudo-Anosov flows. arXiv preprint arXiv:2211.10505, 2022 - https://doi.org/10.48550/arXiv.2211.10505
- BARTHELMÉ, Thomas, FENLEY, Sergio, et MANN, Kathryn. Anosov flows with the same periodic orbits. arXiv preprint arXiv:2308.02098, 2023. - https://doi.org/10.48550/arXiv.2308.02098
- BARTHELMÉ, Thomas, BONATTI, Christian, et MANN, Kathryn. Non-transitive pseudo-Anosov flows. arXiv preprint arXiv:2411.03586, 2024. - https://doi.org/10.48550/arXiv.2411.03586
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