A h-principle for conformal symplectic structures

Appears in collection : Giroux 60 - Convexity in contact and symplectic topology

Any non-degenerate 2-form can be homotoped to a locally conformal symplectic structure whose Lee form can be chosen to be any non-vanishing closed 1-form. Each component of the boundary can be chosen to be concave or convex and to inherit a given overtwisted contact structure. On the other hand, for codimension one foliations, a leafwise conformal symplectic structure whose Lee form coincides with the holonomy 1-form yields a contact structure. Unfortunately, the h-principle described above does not admit a foliated version unless the ambient manifold has a non-empty boundary. This is a joint work with Gaël Meigniez.