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arXiv:math/0605493 [math.GT]AbstractReferencesReviewsResources

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

Robert Myers

Published 2006-05-17, updated 2006-05-18Version 2

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.

Comments: 6 pages
Categories: math.GT, math.GR
Subjects: 57N10, 57M05
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