Positive surface group representations in PO(p,q)

Jonas Beyrer; Beatrice Pozzetti

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arXiv · 2106.14725

Positive surface group representations in PO(p,q)

Jonas Beyrer·Beatrice Pozzetti

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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.

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Jonas Beyrer, Beatrice Pozzetti. 2021-06-28. Positive surface group representations in PO(p,q). https://arxiv.org/abs/2106.14725

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