Cusp singularities in integrable Hamiltonian fibrations


Our paper with Andrea Giacobbe on cusp singularities of integrable Hamiltonian fibrations has now been accepted for publication in Nonlinearity. Andrea and I tried to understand how cusp singularities fit together in the momentum domain of integrable Hamiltonian fibrations. It turns out that when two cusp singularities are connected by a curve of hyperbolic singularities there are locally two possible topologies of the unfolded momentum domain that we call pleat and flap. The pleat topology is associated to bidromy while the flap topology is associated to non-trivial Hamiltonian monodromy. For more details you can check the paper.