Positive surface group representations in PO(p,q)

Abstract

We show that $\hat{I}˜$-positive Anosov representations $\ddot{I}:\hat{I}“\to \mathsf{PO}(p,q)$ of a surface group $\hat{I}“$ 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 $\hat{I}˜$-positive Anosov representations $\ddot{I}:\hat{I}“\to \mathsf{PO}(p,q)$ form connected components of character varieties.

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