On possible values of the signature of flat symplectic bundles over surfaces with boundary

Inkang Kim, Pierre Pansu, Xueyuan Wan

We show that every integer in the interval $[2p\ddot{I}‡(\hat{I}\pounds ),-2p\ddot{I}‡(\hat{I}\pounds )]$ is achieved by the signature of a rank $2p$ flat symplectic bundle over a surface with boundary $\hat{I}\pounds$. When $p=1$,…