Chern–Weil Maslov index and its orbifold analogue

Abstract

We give Chern-Weil definitions of the Maslov indices of bundle pairs over a Riemann surfacewith boundary, which consists of symplectic vector bundle onand a Lagrangian subbundle on @� as well as its gen- eralization for transversely intersecting Lagrangian boundary conditions. We discuss their properties and relations to the known topological definitions. As a main application, we extend Maslov index to the case with orbifold inte- rior singularites, via curvature integral, and find also an analogous topological definition in these cases.