Profinite detection of 3-manifold decompositions

Abstract

The profinite completion of the fundamental group of a closed, orientable $3$-manifold determines the Kneser--Milnor decomposition. If $M$ is irreducible, then the profinite completion determines the Jaco--Shalen--Johannson decomposition of $M$.

20 pages, no figures. v2: Added Corollary C. v3: Referee's comments incorporated. This is the version accepted for publication

References in corpus (4)

• Some 3-manifold groups with the same finite quotients
• The profinite completions of knot groups determine the Alexander polynomials
• The profinite completion of $3$-manifold groups, fiberedness and the Thurston norm
• Profinite rigidity, fibering, and the figure-eight knot

Cited by in corpus (11)

• The profinite completions of knot groups determine the Alexander polynomials
• Finite-volume hyperbolic 3-manifolds are almost determined by their finite quotient groups
• Profinite rigidity for twisted Alexander polynomials
• On profinite rigidity amongst free-by-cyclic groups I: the generic case
• Generalized Stallings' decomposition theorem for pro-$p$ groups
• Mapping classes are almost determined by their finite quotient actions
• Alexander polynomial, Dijkgraaf-Witten invariant, and Seifert fibred surgery
• On the profinite distinguishability of hyperbolic Dehn fillings of finite-volume 3-manifolds
• Problems on handlebody groups
• Profinite almost rigidity in 3-manifolds
• Finite quotients, arithmetic invariants, and hyperbolic volume