# Homogénéisation symplectique et Applications de la théorie des faisceaux à la topologie symplectique

Abstract : In a first part, we develop the theory of symplectic homogenezation and its application to the Aubry Mather theory and also to symplectic rigidity. Spectral invariants are the main tool in this work. In a second part, we recall all the new applications from sheaves theoretic methods to the study of non-displacability problem . We formulate what we think to be the equivalent object to the lagrangian Floer homology and its spectral invariants. Then, using this tools, we prove non-displacability of non exact lagrangian submanifolds into the cotangent bundle. After, we discuss the applications to $C^0$ symplectic topology and to non smooth optimization.
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Cited literature [39 references]

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Submitted on : Tuesday, January 22, 2013 - 11:13:36 PM
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• HAL Id : pastel-00780016, version 1

### Citation

Nicolas Vichery. Homogénéisation symplectique et Applications de la théorie des faisceaux à la topologie symplectique. Géométrie symplectique [math.SG]. Ecole Polytechnique X, 2012. Français. ⟨pastel-00780016⟩

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