Small PSL(2, 𝔽) representations of Seifert fiber space groups

09/12/2022

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by   Neil R Hoffman, et al.

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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 PSL(2, 𝔽) quotient where |𝔽| < c(2^20t3^120t) 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.