English

Some 3-manifold groups with the same finite quotients

Geometric Topology 2014-10-06 v2

Abstract

We give examples of closed, oriented 3-manifolds whose fundamental groups are not isomorphic, but yet have the same sets of finite quotient groups; hence the same profinite completions. We also give examples of compact, oriented 3-manifolds with non-empty boundaries whose fundamental groups though isomorphic have distinct peripheral structures, but yet have the same sets of finite peripheral pair quotients (defined below). The examples are Seifert Fibered Spaces with zero rational Euler number; moreover most of these manifolds give rise to such examples.

Keywords

Cite

@article{arxiv.1409.3509,
  title  = {Some 3-manifold groups with the same finite quotients},
  author = {John Hempel},
  journal= {arXiv preprint arXiv:1409.3509},
  year   = {2014}
}

Comments

10 pages. Reference to related result added. Several typos, some involving incorrect and/or missing symbols corrected

R2 v1 2026-06-22T05:54:41.466Z