On embedding the fundamental group of a 3-manifold in one of its knot groups

Robert Myers

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On embedding the fundamental group of a 3-manifold in one of its knot groups

Robert Myers

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Abstract

This paper gives necessary and sufficient conditions on a compact, connected, orientable 3-manifold M for it to contain a knot K such that M-K is irreducible and pi_1(M) embeds in pi_1(M-K). This result provides counterexamples to a conjecture of Lopes and Morales and characterizes those orientable 3-manifolds for which it is true.

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Robert Myers. 2006-05-18. On embedding the fundamental group of a 3-manifold in one of its knot groups. https://arxiv.org/abs/math/0605493

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