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.

翻译：让$M 成为非美方基本组的Seifit纤维空间, 并接受使用$t$四重体的三角定位。 我们显示有非美方$\ text{PSL}( 2, \ mathbb{F}) 的商数, 其中美方$*mathbb F ⁇ < c( 2 ⁇ 20t} 3 ⁇ 120t}) 的绝对常数 $c>0, 并以此来显示镜头空间识别问题在于用于Seifit纤维空间输入的 CoNP。 我们最后要讨论一下我们的结果, 将镜头空间与其他300美元的皮层区别开来。