Homotopy invariants for solutions to symplectic Monge Ampère equations (Q1318257)

A symplectic Monge Ampère equation is defined to be an auxiliary 2-form on the cotangent bundle of \(\mathbb{R}^ 2\). A Lagrangian solution (maybe multivalued) is a Lagrangian surface annihilating the above form. The author makes a topological analysis of Lagrangian solutions, based on two topological invariants: Maslov class and polarization index. Two particular cases are under consideration: when the equation is homotopically trivial and when it changes its type transversely on a circle bundle. For example, he derives from the analysis of the latter case that the classical gas dynamics equation admits solutions with arbitrary Maslov index or polarization index.