2025 - T2 - WS1 - Higher rank geometric structures, Higgs bundles and physics

Collection 2025 - T2 - WS1 - Higher rank geometric structures, Higgs bundles and physics

Organisateur(s) Canary, Richard ; Garcia-Faide, Elba ; Labourie, François ; Li, Qiongling ; Neitzke, Andrew ; Pozzetti, Beatrice ; Wienhard, Anna
Date(s) 19/05/2025 - 27/05/2025
URL associée https://indico.math.cnrs.fr/event/11569/
2 20

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

De Colin Davalo

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.

Informations sur la vidéo

Bibliographie

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

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