|Title||Quadric bundles applied to non-maximal Higgs bundles|
|Year of Preprint||2016|
We present a survey on the moduli spaces of rank 2 quadric bundles over a compact Riemann surface X. These are objects which generalise orthogonal bundles and which naturally occur through the study of the connected components of the moduli spaces of Higgs bundles over X for the real symplectic group Sp(4,R), with non-maximal Toledo invariant. Hence they are also related with the moduli space of representations of \pi_1(X) in \Sp(4,R). We explain this motivation in some detail.