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Courbes Pseudo-Holomorphes et Transversalité : La Conjecture d'Arnold pour les Sous-Variétés Lagrangiennes Fortement Négatives

Abstract : The main object of this work is to examine how in an almost complex manifold of any dimension a pseudo-holomorphie curve can be factorized through a somewhere injective curve, in order to get some smooth moduli space of curves. One first deals with the easy case of the closed curves, then with curves with boundary in a totally real submanifold. Contrary to a closed curve, a curve with boundary may be neither somewhere injective nor multi-covered. However it is possible to extract from its image another curve somewhere injective but still with boundary in the totally real submanifold. Moreover, if the initial curve is a disc, thèn the extracted disc can be 50 as weIl. As an application, one proves a special case of the Arnold conjecture for the intersection of a Lagrangian submanifold and its Hamiltonian isotopies in a symplectie manifold.
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http://docnum.univ-lorraine.fr/prive/SCD_T_1999_0202_LAZZARINI.pdf
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Submitted on : Thursday, March 29, 2018 - 10:50:52 AM
Last modification on : Tuesday, January 12, 2021 - 1:55:04 PM

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  • HAL Id : tel-01747093, version 1

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Laurent Lazzarini. Courbes Pseudo-Holomorphes et Transversalité : La Conjecture d'Arnold pour les Sous-Variétés Lagrangiennes Fortement Négatives. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 1999. Français. ⟨NNT : 1999NAN10202⟩. ⟨tel-01747093⟩

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