Positive surface group representations in $\mathsf{PO}(p,q)$

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 (2014), that $\Theta$-positive Anosov representations $\rho :\Gamma \to \mathsf{PO}(p,q)$ form connected components of character varieties.