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

Neil R Hoffman; Kathleen L Petersen

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

Geometric Topology 2022-09-13 v1 Computational Complexity

Authors: Neil R Hoffman , Kathleen L Petersen

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.

Keywords

seifert fiber space psl(2,f) representation lens space recognition coNP triangulation 3-manifold

Cite

@article{arxiv.2209.05478,
  title  = {Small $\text{PSL}(2, \mathbb{F})$ representations of Seifert fiber space groups},
  author = {Neil R Hoffman and Kathleen L Petersen},
  journal= {arXiv preprint arXiv:2209.05478},
  year   = {2022}
}

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15 pages, 1 figure

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

Abstract

Keywords

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