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arXiv · 2409.06294

Positivity, cross-ratios and the Collar Lemma

Jonas Beyrer·Olivier Guichard·François Labourie·Beatrice Pozzetti·Anna Wienhard
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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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Jonas Beyrer, Olivier Guichard, François Labourie, Beatrice Pozzetti, Anna Wienhard. 2024-09-10. Positivity, cross-ratios and the Collar Lemma. https://arxiv.org/abs/2409.06294

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