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A collar lemma for partially hyperconvex surface group representations
Transactions of the American Mathematical Society ( IF 1.3 ) Pub Date : 2021-07-15 , DOI: 10.1090/tran/8453
Jonas Beyrer , Beatrice Pozzetti

Abstract:We show that a collar lemma holds for Anosov representations of fundamental groups of surfaces into $SL(n,\mathbb {R})$ that satisfy partial hyperconvexity properties inspired from Labourie’s work. This is the case for several open sets of Anosov representations not contained in higher rank Teichmüller spaces, as well as for $\Theta$-positive representations into $SO(p,q)$ if $p\geq 4$. We moreover show that ‘positivity properties’ known for Hitchin representations, such as being positively ratioed and having positive eigenvalue ratios, also hold for partially hyperconvex representations.


中文翻译:

部分超凸曲面群表示的领引理

摘要:我们证明了一个领引理适用于表面基本群的 Anosov 表示到 $SL(n,\mathbb {R})$ 中,满足部分超凸性属性,灵感来自 Labourie 的工作。这是不包含在更高阶 Teichmüller 空间中的几个开放的 Anosov 表示集的情况,以及如果 $p\geq 4$ 到 $SO(p,q)$ 中的 $\Theta$-positive 表示。此外,我们还表明 Hitchin 表示已知的“正性属性”,例如正比和具有正特征值比,也适用于部分超凸表示。
更新日期:2021-09-21
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