Profinite Rigidity, Fibering, and the Figure-eight Knot
نویسنده
چکیده
We establish results concerning the profinite completions of 3-manifold groups. In particular, we prove that the complement of the figure-eight knot SrK is distinguished from all other compact 3-manifolds by the set of finite quotients of its fundamental group. In addition, we show that if M is a compact 3-manifold with b1(M) = 1, and π1(M) has the same finite quotients as a free-by-cyclic group Fr ⋊ Z, then M has non-empty boundary, fibres over the circle with compact fibre, and π1(M) ∼= Fr ⋊ψ Z for some ψ ∈ Out(Fr).
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