Conformal Symplectic Structures, Foliations and Contact Structures

Melanie Bertelson , Gael Meigniez (1)

1 I2M - Institut de Mathématiques de Marseille

This paper presents two existence h-principles, the first for conformal symplectic structures on closed manifolds, and the second for leafwise conformal symplectic structures on foliated manifolds with non empty boundary. The latter h-principle allows to linearly deform certain codimension-1 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.

Mots clés: conformal symplectic; symplectic cobordism; foliation; contact; h-principle

Domaines: Topologie géométrique [math.GT]

Melanie Bertelson, Gael Meigniez. Conformal Symplectic Structures, Foliations and Contact Structures. 2021. ⟨hal-03341749⟩