# MathSciDoc: An Archive for Mathematician ∫

#### Symplectic Geometrymathscidoc:1912.43241

arXiv preprint arXiv:1202.0556, 2012.2
We give Chern-Weil definitions of the Maslov indices of bundle pairs over a Riemann surface with boundary, which consists of symplectic vector bundle on and a Lagrangian subbundle on\partial as well as its generalization 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 interior singularites, via curvature integral, and find also an analogous topological definition in these cases.