Asian Journal of Mathematics

Volume 20 (2016)

Number 1

Chern–Weil Maslov index and its orbifold analogue

Pages: 1 – 20



Cheol-Hyun Cho (Department of Mathematical Sciences, Research Institute of Mathematics, Seoul National University, Seoul, Korea)

Hyung-Seok Shin (School of Mathematics, Korea Institute for Advanced Study, Seoul, Korea)


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 singularities, via curvature integral, and find also an analogous topological definition in these cases.


Maslov index, Chern–Weil theory, holomorphic disks, orbifolds

2010 Mathematics Subject Classification

53D12, 57R18

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Published 28 January 2016