I'm looking at the following topology qualifying exam question:
Let K be a knot in $S^3$. Construct a map $f: S^2 \vee S^1 \rightarrow (\mathbb{R}^3 - K)$ that induces an isomorphism of integral homology.
My biggest problem is I'm not really sure what a knot in $S^3$ is. Is it just an embedding of a circle into $S^3$? Is there a nice reference for these? Also, a hint as to what the map should be would be appreciated. Should I define it on a cellular level?