I recall my Professor having stated something along the lines of the following, but I am not quite certain about the precise statement she gave:
Let $M$ be a compact, orientable 3 manifold with non-empty boundary. Then $M$ can be embedded in $\mathbb S^3$. More precisely, $M$ is diffeomorphic to $\mathbb S^3 \setminus N$, where $N$ is a finite collection of embedded open handlebodies.
Is this statement true? If not, what would be an easy counterexample, and does there still exists a weaker form of the statement that is actually true ? Any help is appreciated.