Non-maximal Anosov representations from surface groups to ${\mathrm{SO}}_0(2,3)$

Abstract

We prove the representation given by a stable $\hat{I}{\pm }_1$-cyclic parabolic ${\mathrm{SO}}_0(2,3)$-Higgs bundle through the non-Abelian Hodge correspondence is $\{\hat{I}{\pm }_2\}$-almost dominated. This is a generalization of Filip's result on weight $3$ variation of Hodge structures and answers a question asked by Collier, Tholozan and Toulisse.

Final version, to appear in Mathematische Annalen. 35 pages, comments are very welcome