# Level sets of Hamiltonians of S^1 actions

Suppose that $(M,\omega)$ is a (connected compact) symplectic manifold with a Hamiltonian $S^1$-action given by Hamiltonian $H$. I would like to find a reference for the fact that every level set of $H$ is connected. I tried to find this statement in McDuff Salamon, but could not.

-
This follows directly, by a standard argument, from the fact that $H$ is a Morse-Bott function, all of whose critical manifolds have even index (and co-index). –  Robert Bryant Jul 20 '13 at 13:24
Robert, thank you for your comment! I was wondering if there is some textbook where this is written... –  aglearner Jul 20 '13 at 13:43