Certifying Anosov representations

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2026-03-27 DOI:10.1112/blms.70342

J. Maxwell Riestenberg

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Abstract

By providing new finite criteria which certify that a finitely generated subgroup of $SL (d, R)$ or $SL (d, C)$ is projective Anosov, we obtain a practical algorithm to verify the Anosov condition. We demonstrate on a surface group of genus 2 in $SL (3, R)$ by verifying the criteria for all words of length 8. The previous version required checking all words of length 2 million.

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证明Anosov陈述

通过提供新的有限准则来证明SL (d)的有限生成子群R)$ \operatorname{SL}(d,\operatorname{\mathbb {R}})$或SL (d， C)$ \operatorname{SL}(d,\mathbb {C})$是投影的Anosov，给出了一种验证Anosov条件的实用算法。在SL (3， R)$ \ mathm {SL}(3,\mathbb {R})$中，我们通过验证所有长度为8的词的标准来证明属2的曲面群。以前的版本要求检查长度为200万的所有单词。

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