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Simple Knots in Compact, Orientable 3-Manifolds
Transactions of the American Mathematical Society
A simple closed curve J in the interior of a compact, orientable 3-manifold M is called a simple knot if the closure of the complement of a regular neighborhood of J in M is irreducible and boundary-irreducible and contains no non-boundary-parallel, properly embedded, incompressible annuli or tori. In this paper it is shown that every compact, orientable 3-manifold M such that 9AÍ contains no 2-spheres contains a simple knot (and thus, from work of Thurston, a knot whose complement isdoi:10.2307/1999193 fatcat:zgo7vcdakzhmjpsl3vh5jr5m3y