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Positivity, cross-ratios and the Collar Lemma

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arxiv 2409.06294 v1 pith:ADS2VING submitted 2024-09-10 math.DG math.GR

Jonas Beyrer , Olivier Guichard (UNISTRA) , François Labourie (UniCA) , Beatrice Pozzetti , Anna Wienhard This is my paper · ORCID
classification math.DGmath.GR
keywords positivecollarcross-ratioslemmarepresentationsthetaassociatedclosed
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abstract

We prove that $\Theta$-positive representations of fundamental groups of surfaces (possibly cusped or of infinite type) satisfy a collar lemma, and their associated cross-ratios are positive. As a consequence we deduce that $\Theta$-positive representations form closed subsets of the representation variety.

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Cited by 1 Pith paper

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  1. Transverse groups preserving proper domains in flag manifolds

    math.RT 2025-07 reject novelty 8.0 of 10

    Transverse groups preserving proper domains in flag manifolds must have limit triples of a single type (Maslov index zero in the tube-type case), but the proof of this key claim contains a false step.

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