Workshop on the h-principle and beyond

Abstract : We describe a construction of a locally conformal symplectic structure homotopic to any given non-degenerate 2-form and whose Lee form can be any non-exact 1-form. Moreover, each connected component of the boundary, if any, may be chosen to be concave or convex and to inherit a given overtwisted contact structure. On the other hand, for a codimension one foliations, a leafwise locally conformal symplectic structure whose Lee form coincides with the holonomy 1-form of the foliation 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 that intersects all the leaves (plus some other rather natural conditions). This is a joint work with Gaël Meigniez.