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

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

2006-05-17

arxiv.org/abs/math/0605493v2

Mathematics

Geometric Topology

6 pages

Scientific paper

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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