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

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.

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Publication Details

Journal
Journal of the European Mathematical Society
Published
2024-11-06
DOI
https://doi.org/10.4171/jems/1560
Citations
3
Primary Topic
Geometric and Algebraic Topology
Type
article
Field-Weighted Citation Impact
3.04
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article

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

Jonas Beyrer, Maria Beatrice Pozzetti
3 citations
Journal of the European Mathematical Society
Geometric and Algebraic Topology
3.04
article

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

Jonas Beyrer, Maria Beatrice Pozzetti
article en
3 citations

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.

Journal of the European Mathematical SocietyVol. 28(6)
LMU Klinikum (DE), Ludwig-Maximilians-Universität München (DE), University of Bologna (IT)
Reduced inequalities
Openalex Percentile: Top 8%
Geometric and Algebraic Topology
3.04
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