Groups of Anosov-like homeomorphisms and foliations of the plane - lecture 1 | Vidéo | Carmin.tv

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Groups of Anosov-like homeomorphisms and foliations of the plane - lecture 1

By Kathryn Mann

Appears in collection : Foliations and Diffeomorphism Groups / Feuilletages et Groupes de Difféomorphisme

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.

Information about the video

Date of recording 09/12/2024
Date of publication 10/01/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20275003
Cite this video Mann, Kathryn (09/12/2024). Groups of Anosov-like homeomorphisms and foliations of the plane - lecture 1. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20275003
URL https://dx.doi.org/10.24350/CIRM.V.20275003

Domain(s)

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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