2021 - T2 - Symplectic topology, contact topology and interactions

Collection 2021 - T2 - Symplectic topology, contact topology and interactions

Organizer(s) Colin, Vincent ; Humilière, Vincent ; Massot, Patrick ; Niederkrüger, Klaus ; Oancea, Alexandru ; Vaugon, Anne

Date(s) 19/04/2021 - 16/07/2021

linked URL https://indico.math.cnrs.fr/event/5767/

00:00:00 / 00:00:00

42 45

Non-squeezing of Legendrian knots into neighbourhoods of non-Legendrians and C^0 contactomorphisms

By Georgios Dimitroglou Rizell

We discuss joint work with M. Sullivan where we show that a contactomorphism cannot squeeze some fixed Legendrian knot into an arbitrarily small neighbourhood of a non-Legendrian knot, under the additional constraint that the two knots become isotopic inside the neighbourhood, and that the contact manifold is tight. The techniques used are Giroux's theory of convex surfaces combined with Honda's study of solid tori with convex boundary. A corollary is that a smooth image of a Legendrian under a C^0-contactomorphism is again Legendrian (here tightness is not needed).

Information about the video

Date of recording 02/07/2021
Date of publication 02/07/2021
Institution IHP
Language English
Audience Researchers
Format MP4

Domain(s)

Symplectic Geometry

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