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Positive Legendrian isotopies and Floer theory

Banff International Research Station for Mathematical Innovation and Discovery

In a cooriented contact manifold, a positive Legendrian isotopy is a Legendrian isotopy evolving in the positive transverse direction to the contact plane. Their global behavior differs from the one of Legendrian isotopy and is closer to the one of propagating waves. In this talk I will explain how to use information in the Floer complex associated to a pair of Lagrangian cobordisms (recently constructed in a collaboration with G. Dimitroglou Rizell, P. Ghiggini and R. Golovko) to give obstructions to certain positive loops of some Legendrian submanifolds. This will recover previously known obstructions and exhibit more examples. This is work in progress with V. Colin and G. Dimitroglou Rizell.

Mathematics; Manifolds and cell complexes; Global analysis, analysis on manifolds; Low dimensional topology

video/mp4

Author affiliation: Université de Nantes

2016-09-21

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59243

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/