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 $g\ge 2$ 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.

arXiv comment24 pages. v2: some improvements and corrections; main results unchanged. arXiv admin note: text overlap with arXiv:1004.0245