Convexity in contact and symplectic topology

A h-principle for conformal symplectic structures

4 juil. 2022, 11:00

1h

Amphithéâtre Hermite (Institut Henri Poincaré)

Orateur

Mélanie Bertelson (Université Libre de Bruxelles)

Description

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.