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Conformal Symplectic structures, Foliations and Contact Structures

par Bertelson, Mélanie ;Meigniez, Gaël GM
Référence Journal of symplectic geometry, page (40)
Publication A Paraître, 2023-01-01

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Résumé :

This paper presents two existence h-principles, the first one for conformal symplectic structures on closed manifolds, and the second one for leafwise conformal symplectic structures on manifolds with non empty boundary. The latter h-principle allows to linearly deform certain codimension one foliations to contact structures. These results are essentially applications of the Borman-Eliashberg-Murphy h-principle for overtwisted contact structures and of the Eliashberg-Murphy symplectization of cobordisms, together with tools pertaining to foliated Morse theory, which are elaborated here.