Positive surface group representations in PO(p,q)

Abstract

We show that $\Theta$-positive Anosov representations $\rho :\Gamma \to \mathsf{PO}(p,q)$ of a surface group $\Gamma$ satisfy root versus weight collar lemmas for all the Anosov roots, and are positively ratioed with respect to all such roots. We deduce from this, using a result of Beyrer-Pozzetti (2024), that $\Theta$-positive Anosov representations $\rho :\Gamma \to \mathsf{PO}(p,q)$ form connected components of character varieties.

44 pages, 3 figures. Version accepted for pubblication in Journal of the European Mathematical Society. Comments welcome!

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Cited by in corpus (3)

• Positivity and representations of surface groups
• Degenerations of k-positive surface group representations
• Fiber bundles associated with Anosov representations