Small $\text{PSL}(2, \mathbb{F})$ representations of Seifert fiber space groups

Neil R Hoffman; Kathleen L Petersen

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arXiv · 2209.05478

Small $\text{PSL}(2, \mathbb{F})$ representations of Seifert fiber space groups

Neil R Hoffman·Kathleen L Petersen

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Abstract

Let $M$ be a Seifert fiber space with non-abelian fundamental group and admitting a triangulation with $t$ tetrahedra. We show that there is a non-abelian $\text{PSL}(2, \mathbb{F})$ quotient where $|\mathbb F| < c(2^{20t}3^{120t})$ for an absolute constant $c>0$ and use this to show that the lens space recognition problem lies in coNP for Seifert fiber space input. We end with a discussion of our results in the context of distinguishing lens spaces from other $3$--manifolds more generally.

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Neil R Hoffman, Kathleen L Petersen. 2022-09-12. Small $\text{PSL}(2, \mathbb{F})$ representations of Seifert fiber space groups. https://arxiv.org/abs/2209.05478

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