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Groups of Anosov-like homeomorphisms and foliations of the plane - lecture 1
Multi angle
Authors : ... (Author of the conference)
... (Publisher )
37D05 - Hyberbolic orbits and sets
57M60 - Group actions in low dimensions
57S25 - Groups acting on specific manifolds
... (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
Language : EnglishAvailable 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 DifféomorphismeDates : 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: (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 |
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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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