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 consisting of Zariski dense representations. This also allows a comparison between the invariants for maximal Higgs bundles and the topological invariants for Anosov representations constructed by Guichard and Wienhard.

中文翻译：

---

模型希格斯束在 Sp(4, ℝ) 字符变体的特殊组件中

我们在黎曼曲面的连通总和上建立了希格斯束的粘合结构Sp(4, ℝ)- 使用相关椭圆算子线性化的希钦方程。该结构可用于提供所有模型中的希格斯束2G - 3最大的特殊组件Sp(4, ℝ)-Higgs 束模空间，对应于仅由 Zariski 密集表示组成的组件。这也允许在最大希格斯束的不变量和由 Guichard 和 Wienhard 构建的 Anosov 表示的拓扑不变量之间进行比较。