Taut foliations through a contact lens | Vidéo | Carmin.tv

00:00:00 / 00:00:00

Taut foliations through a contact lens

By Thomas Massoni

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

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.

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.20275203
Cite this video Massoni, Thomas (09/12/2024). Taut foliations through a contact lens. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20275203
URL https://dx.doi.org/10.24350/CIRM.V.20275203

Domain(s)

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

MSC codes

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow

Copyright Carmin.tv 2025

Give feedback