Positive surface group representations in PO(p,q)

2021/06/28 by Jonas Beyrer, Beyrer, Jonas, Beatrice Pozzetti +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2106.14725

openalex publication_date 2021/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that Θ-positive Anosov representations ρ:Γ→\sf PO(p,q) of a surface group Γ 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-positive Anosov representations ρ:Γ→\sf PO(p,q) form connected components of character varieties.

Citations

• Degenerations of k-positive surface group representations

Cited by

• Positivity and Non-commutativity

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• A collar lemma for partially hyperconvex surface group representations
• Positivity, cross-ratios and the Collar Lemma
• Positively ratioed representations
• Simple Anosov representations of closed surface groups
• Degenerations of k-positive surface group representations