# Sous-variétés lagrangiennes monotones

Abstract : The monotonicity condition for Lagrangian submanifolds was introduced by Oh in 1993. This is a relative version of a condition defined by Floer for symplectic manifolds. These conditions make possible the definition of Floer type homologies, especially of the Lagrangian Floer homology, which is very useful for the study of Lagrangian embeddings.

In this thesis, we study the monotonicity hypothesis in two directions. One direction is the study of a new family of examples of monotone symplectic manifolds and their monotone Lagrangian submanifolds. This family of examples is constructed by symplectic cut of the cotangent bundle of manifolds endowed with a free circle action. A second aspect is the construction of a Floer-Novikov type of homology for Lagrangian submanifolds which are called monotone on the loops. We deduce new results on Lagrangian embeddings which are monotone on the loops in the cotangent bundle of manifolds which are the total space of a fibration over the circle.
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https://tel.archives-ouvertes.fr/tel-00286624
Contributor : Agnès Gadbled <>
Submitted on : Thursday, June 26, 2008 - 11:23:35 AM
Last modification on : Friday, June 19, 2020 - 9:10:04 AM
Long-term archiving on: : Friday, November 25, 2016 - 10:22:19 PM

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• HAL Id : tel-00286624, version 3

### Citation

Agnès Gadbled. Sous-variétés lagrangiennes monotones. Mathématiques [math]. Université Louis Pasteur - Strasbourg I, 2008. Français. ⟨tel-00286624v3⟩

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