Some 3-manifold groups with the same finite quotients

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.

arXiv comment10 pages. Reference to related result added. Several typos, some involving incorrect and/or missing symbols corrected

References in corpus (1)

• A MILP model for an extended version of the Flexible Job Shop Problem

Cited by in corpus (8)

• Profinite detection of 3-manifold decompositions
• Profinite rigidity and surface bundles over the circle
• The profinite completions of knot groups determine the Alexander polynomials
• Finite-volume hyperbolic 3-manifolds are almost determined by their finite quotient groups
• A remark on torsion growth in homology and volume of 3-manifolds
• Finite quotients, arithmetic invariants, and hyperbolic volume
• Mapping classes are almost determined by their finite quotient actions
• Virtual pro-$p$ properties of 3-manifold groups