Extending compact Hamiltonian ${\mathbb{S}}^1$-spaces to integrable systems with mild degeneracies in dimension four

Sonja Hohloch, Joseph Palmer

Given any compact connected four dimensional symplectic manifold $(M,\omega )$ and smooth function $J:M\to \mathbb{R}$ which generates an effective ${\mathbb{S}}^1$-action, we show t…