Excellent knot representative theorem
= Excellent knot representative theorem
In a compact connected orientable <three-manifold> with no spherical boundary components, every embedded <knot> is homotopic to a <knot> with an <excellent three-manifold> as exterior. In particular this can preserve the generator class in $S^1\times S^2$, or the <winding number of a satellite pattern> one class in a <solid torus>. Homotopy here is weaker than <isotopy>.