English
Taut foliations through a contact lens
Multi angle
Auteurs : Massoni, Thomas (Auteur de la conférence)
CIRM (Editeur )
37D10 - Invariant manifold theory
57R30 - Foliations; geometric theory
57K33 - Contact structures in 3 dimensions
CIRM (Editeur )
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Résumé :
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.
Mots-Clés : Taut foliations; contact pairs; branching foliations
Codes MSC : Mots-Clés : Taut foliations; contact pairs; branching foliations
37D10 - Invariant manifold theory
57R30 - Foliations; geometric theory
57K33 - Contact structures in 3 dimensions
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 10/01/2025 Date de Captation : 09/12/2024 Sous Collection : Research talks Catégorie arXiv : Symplectic Geometry ; Dynamical Systems ; Geometric Topology Domaine(s) : Systèmes Dynamiques & EDO ; Géométrie ; Topologie Format : MP4 (.mp4) - HD Durée : 01:02:04 Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-12-09_Massoni.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : Foliations and Diffeomorphism Groups / Feuilletages et Groupes de DifféomorphismeOrganisateurs de la Rencontre : Eynard-Bontemps, Hélène ; Meigniez, Gaël ; Nariman, Sam ; Yazdi, Mehdi Dates : 09/12/2024 - 13/12/2024 Année de la rencontre : 2024 URL de la Rencontre : https://conferences.cirm-math.fr/3082.html
Données de citation
DOI : 10.24350/CIRM.V.20275203Citer cette vidéo: 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 |
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Bibliographie
- 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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