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Taut foliations through a contact lens
Multi angle
Authors : Massoni, Thomas (Author of the conference)
CIRM (Publisher )
37D10 - Invariant manifold theory
57R30 - Foliations; geometric theory
57K33 - Contact structures in 3 dimensions
CIRM (Publisher )
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Abstract :
In the late '90s, Eliashberg and Thurston established a remarkable connection between foliations and contact structures in dimension three: any co-oriented, aspherical foliation on a closed, oriented 3-manifold can be approximated by both positive and negative contact structures. Additionally, if the foliation is taut then its contact approximations are tight. In this talk, I will present a converse result on constructing taut foliations from suitable pairs of contact structures. While taut foliations are rather rigid objects, this viewpoint reveals some degree of flexibility and offers a new perspective on the L-space conjecture. A key ingredient is a generalization of a result of Burago and Ivanov on the construction of branching foliations tangent to continuous plane fields, which might be of independent interest.
Keywords : Taut foliations; contact pairs; branching foliations
MSC Codes : Keywords : Taut foliations; contact pairs; branching foliations
37D10 - Invariant manifold theory
57R30 - Foliations; geometric theory
57K33 - Contact structures in 3 dimensions
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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 talks arXiv category : Symplectic Geometry ; Dynamical Systems ; Geometric Topology Mathematical Area(s) : Dynamical Systems & ODE ; Geometry ; Topology Format : MP4 (.mp4) - HD Video Time : 01:02:04 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-12-09_Massoni.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.20275203Cite this video as: Massoni, Thomas (2024). Taut foliations through a contact lens. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20275203 URI : http://dx.doi.org/10.24350/CIRM.V.20275203 |
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] Groups of Anosov-like homeomorphisms and foliations of the plane - lecture 1 / Author of the conference Mann, Kathryn.
- [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
- MASSONI, Thomas. Taut foliations and contact pairs in dimension three. arXiv preprint arXiv:2405.15635, 2024. - https://doi.org/10.48550/arXiv.2405.15635
- BOWDEN, Jonathan. Approximating c 0-foliations by contact structures. Geometric and Functional Analysis, 2016, vol. 26, p. 1255-1296. - https://doi.org/10.1007/s00039-016-0387-2
- BURAGO, Dmitri et IVANOV, Sergei. Partially hyperbolic diffeomorphisms of 3-manifolds with abelian fundamental groups. J. Mod. Dyn, 2008, vol. 2, no 4, p. 541-580. - https://doi.org/10.3934/jmd.2008.2.541
- COLIN, Vincent et FIRMO, Sebastiao. Paires de structures de contact sur les variétés de dimension trois. Algebraic & Geometric Topology, 2011, vol. 11, no 5, p. 2627-2653. - http://dx.doi.org/10.2140/agt.2011.11.2627
- COLIN, Vincent, KAZEZ, William H., et ROBERTS, Rachel. Taut foliations. Communications in Analysis and Geometry, 2019, vol. 27, no 2, p. 357-375. - https://dx.doi.org/10.4310/CAG.2019.v27.n2.a4
- ELIASHBERG, Yakov et THURSTON, William P. Confoliations. American Mathematical Soc., 1998. - https://doi.org/10.1090/ulect/013
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