P. Pansu

On possible values of the signature of flat unitary bundles over compact surfaces

We determine all possible signatures of flat Hermitian bundles over compact, connected, oriented surfaces of positive genus with nonempty boundary. If $\Sigma_{g,n}$ has genus $g\geq 1$ and $n\geq 1$ boundary components, then the signatures arising from representations $\pi_1(\Sigma_{g,n})\to\mathrm{U}(p,q)$ are exactl...