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

2006/05/17 by Myers, Robert
#57M05 #57N10 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.math/0605493

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 pi₁(M) embeds in pi₁(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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