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 $[2p\chi (\Sigma ),-2p\chi (\Sigma )]$ is achieved by the signature of a rank $2p$ flat symplectic bundle over a surface with boundary $\Sigma$. When $p=1$, one…