Model Higgs bundles in exceptional components of the $\text{Sp(4}\text{,}\mathbb{R}\text{)}$-character variety

Georgios Kydonakis (1)

1 MPI - Max-Planck-Institut für Mathematik

We establish a gluing construction for Higgs bundles over a connected sum of Riemann surfaces in terms of solutions to the $\text{Sp(4}\text{,}\mathbb{R}\text{)}$-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 $\text{Sp(4}\text{,}\mathbb{R}\text{)}$-Higgs bundle moduli space, which correspond to components solely consisted 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 O. Guichard and A. Wienhard.

Mots clés: Higgs bundle; character variety; gluing construction; Hitchin equations; elliptic operator

Domaines: Géométrie différentielle [math.DG]; Géométrie algébrique [math.AG]

Georgios Kydonakis. Model Higgs bundles in exceptional components of the $\text{Sp(4}\text{,}\mathbb{R}\text{)}$-character variety. International Journal of Mathematics, 2021, 32 (09), pp.2150067. ⟨10.1142/S0129167X21500671⟩. ⟨hal-02467445v2⟩