Taut foliations through a contact lens

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Taut foliations through a contact lens

Nom de l'orateur
Thomas Massoni
Etablissement de l'orateur
MIT
Date et heure de l'exposé
23-01-2025 - 11:00:00
Lieu de l'exposé
Salle des séminaires
Résumé de l'exposé

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.

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