English

Positive surface group representations in PO(p,q)

Geometric Topology 2024-10-14 v2 Differential Geometry Group Theory

Abstract

We show that Θ\Theta-positive Anosov representations ρ:ΓPO(p,q)\rho:\Gamma\to{\sf PO}(p,q) of a surface group Γ\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 Θ\Theta-positive Anosov representations ρ:ΓPO(p,q)\rho:\Gamma\to{\sf PO}(p,q) form connected components of character varieties.

Keywords

Cite

@article{arxiv.2106.14725,
  title  = {Positive surface group representations in PO(p,q)},
  author = {Jonas Beyrer and Beatrice Pozzetti},
  journal= {arXiv preprint arXiv:2106.14725},
  year   = {2024}
}

Comments

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

R2 v1 2026-06-24T03:40:30.925Z