Positive surface group representations in PO(p,q)

Abstract

We show that $\Theta$-positive Anosov representations $\rho:\Gamma\to{\sf PO}(p,q)$ 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 $\rho:\Gamma\to{\sf PO}(p,q)$ form connected components of character varieties.