A symplectic action of the $m$-torus $\mathbb{T}^m$ on a compact symplectic manifold $(M,\omega)$ yields a moment map $\mu : M\to\mathbb{R}^m$. I would like to study the convexity of the moment map (the Atiyah-Guillemin-Sternberg theorem) which is based on the connectedness of the fibers $\mu^{-1}(c)$.

Thank you!