Abstract
We study local invariants of singular symplectic forms with structurally smooth Martinet hypersurfaces on a 4-dimensional manifold M. We prove that the equivalence class of a germ at p 2 M of a singular symplectic form ! is determined by the Martinet hypersurface, the canonical orientation of it, the pullback of the singular symplectic form to it and the 2-dimensional kernel of ! at p. We also show which germs of closed 2-forms on a 3-dimensional submanifold can be realizable as pullbacks of singular symplectic forms to structurally smooth Martinet hypersurfaces.
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