Positivity, cross-ratios and the Collar Lemma

Jonas BeyrerUNISTRA, Olivier GuichardUNISTRA, François LabourieUniCA, 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.
正向性、交叉比和项圈定理
我们证明了曲面(可能是尖顶曲面或无限型曲面)基本群的$\theta$正表示满足项圈lemma,并且它们相关的交叉比是正的。因此,我们推导出$heta$正表示形成了表示范围的封闭子集。
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