Conformal Symplectic structures, Foliations and Contact Structures

Abstract

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.

This second version is exactly identical to the first one, except for the institution and the email address of the second author

References in corpus (2)

• The plastikstufe - a generalization of the overtwisted disk to higher dimensions
• The foliated Lefschetz hyperplane theorem