(untitled) (JOURNAL OF ADVANCES IN MATHEMATICS, 2018)
We establish a gluing construction for Higgs bundles over a connected sum of Riemann surfaces in terms of solutions to the Sp(4,R)-Hitchin equations using the linearization of a relevant elliptic operator. The construction can be used to provide model Higgs bundles in all the 2g-3 exceptional components of the maximal Sp(4,R)-Higgs bundle moduli space, which correspond to components solely consisted of Zariski dense representations. This alsoallows a comparison between the invariants for maximal Higgs bundles and the topological invariants for Anosov representations constructed by O. Guichard and A. Wienhard.