Degenerations of k $k$ -positive surface group representations

Pub Date : 2024-08-03 DOI:10.1112/topo.12352

Jonas Beyrer, Beatrice Pozzetti

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Abstract

We introduce $k$ -positive representations, a large class of ${1, …, k}$ -Anosov surface group representations into $PGL (E)$ that share many features with Hitchin representations, and we study their degenerations: unless they are Hitchin, they can be deformed to non-discrete representations, but any limit is at least $(k - 3)$ -positive and irreducible limits are $(k - 1)$ -positive. A major ingredient, of independent interest, is a general limit theorem for positively ratioed representations.

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k $k$ 正表面群表示的退化

我们引入了 k 个 $k$ 正表示，这是一大类 { 1 , ... , k }。 $\lbrace 1,\ldots ,k\rbrace$ -Anosov surface group representations into PGL ( E ) $\mathsf {PGL}(E)$，它们与希钦表示有许多共同特征，我们研究了它们的退化：除非它们是希钦表示，否则它们可以变形为非离散表示，但是任何极限至少是 ( k - 3 ) $(k-3)$ -正的，而不可还原极限是 ( k - 1 ) $(k-1)$ -正的。正比例表示的一般极限定理是一个重要的独立内容。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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