Local contractibility of the kernel of the Calabi homomorphism Ham_c^0(M, ω)

Ascertain whether the kernel of the Calabi homomorphism Ham_c^0(M, ω), equipped with the subspace topology induced by Ham_c(M, ω), is locally contractible for general symplectic manifolds (M, ω), including cases with boundary.

Background

The group Ham_c^0(M, ω) arises as the kernel of the Calabi homomorphism on Ham_c(M, ω). The authors construct a quotient topology to ensure local contractibility due to potential non-discreteness of Λ_ω. Whether Ham_c^0(M, ω) is locally contractible under the more natural subspace topology remains unknown in general.