The paper concerns a ${𝒞}^0$-rigidity result for the characteristic foliations in symplectic geometry. A symplectic homeomorphism (in the sense of Eliashberg-Gromov) which preserves a smooth hypersurface also preserves its characteristic foliation.

A Lie version of Turaev’s $\overline{G}$-Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a $𝔤$-quasi-Frobenius Lie algebra for $𝔤$ a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius Lie algebra $(𝔮,\beta )$ together with a left $𝔤$-module structure which acts on $𝔮$ via derivations and for which $\beta$ is $𝔤$-invariant. Geometrically, $𝔤$-quasi-Frobenius Lie algebras are the Lie algebra structures associated to symplectic...