7 problems

Let $(M,c9)$ be a closed symplectic manifold. Write $Hameo(M,c9)$ for the group of Hamiltonian homeomorphisms and $Sympeo_0(M,c9)$ for the identity component of the group of symple…

Calabi extension conjecture. The Calabi homomorphism extends to a homomorphism

Let ${\mathcal P}^{ham}(Sympeo(S^2),id)$ denote the space of continuous Hamiltonian paths from the identity, let $\overline\mu^{path}$ be the extension of the homogeneous Calabi qu…

Let $Hameo(M,\omega)$ be the group of Hamiltonian homeomorphisms and let $Sympeo_0(M,\omega)$ be the identity component of the group of symplectic homeomorphisms. Proper subgroup c…

Let $(M,omega)$ be a closed symplectic manifold. The space $ham_\infty(M,\omega)$ consists of the continuous functions obtained as developing maps of continuous Hamiltonian paths,…

Fathi's conjecture. The homomorphism $\operatorname{Cal}$ extends to a homomorphism on $\operatorname{Hameo}(\Sigma,\omega)$.

Let $(M,\omega)$ be a closed and connected symplectic surface. Denote by $\overline{\operatorname{Ham}}(M,\omega)$ the $C^0$ closure of the group of Hamiltonian diffeomorphisms in…