Connectedness of the moduli of Sp(2p,2q)-Higgs bundles

Abstract: Using the Morse-theoretic techniques introduced by Hitchin, we prove that the moduli space of $\Sp(2p,2q)$-Higgs bundles over a compact Riemann surface of genus $g\geq 2$ is connected. In particular, this implies that the moduli space of representations of the fundamental group of the surface in $\Sp(2p,2q)$ is connected.