  We show that Hamiltonian monodromy of an integrable two degrees of freedom
system with a global circle action can be computed by applying Morse theory to
the Hamiltonian of the system. Our proof is based on Takens's index theorem,
which specifies how the energy-h Chern number changes when h passes a
non-degenerate critical value, and a choice of admissible cycles in
Fomenko-Zieschang theory. Connections of our result to some of the existing
approaches to monodromy are discussed.
