Chern-Weil Maslov index and its orbifold analogue

TL;DR

This paper introduces Chern-Weil formulas for Maslov indices of symplectic bundle pairs with boundary conditions, extends these to orbifold cases with interior singularities, and explores their properties and topological relations.

Contribution

It provides the first Chern-Weil definitions of Maslov indices for orbifold bundle pairs, generalizing classical topological definitions to orbifold settings.

Findings

Chern-Weil formulas for Maslov indices are established.

Extension of Maslov index to orbifold interior singularities.

Topological and curvature-based definitions are shown to coincide.

Abstract

We give Chern-Weil definitions of the Maslov indices of bundle pairs over a Riemann surface \Sigma with boundary, which consists of symplectic vector bundle on \Sigma and a Lagrangian subbundle on \partial{\Sigma} 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.