Deformations of Barbot representations into $\textrm{SL}(3,\mathbb{R})$

De Colin Davalo

Apparaît dans la collection : 2025 - T2 - WS1 - Higher rank geometric structures, Higgs bundles and physics

We consider representations of surface groups into $\textrm{SL}(3,\mathbb{R})$ associated with a certain family of cyclic Higgs bundles. These representations are not in the Hitchin component: they are deformations of representations studied by Barbot. We show that these representations are the holonomy of a geometric structure modelled on the space of full flags in $\mathbb R^3$, and are discrete and faithful in a strong sense: they are Anosov.

We will see how one can associate to these cyclic Higgs bundles a surface in the symmetric space equipped with a parallel distribution of tangent planes, and how this object can be used to construct a geometric structure and prove the Anosov property. This work is a collaboration with Samuel Bronstein.

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Bibliographie

  • Anosov deformations of Barbot representations, Samuel Bronstein and Colin Davalo, arxiv preprint

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