I was told that the conormal bundle $\nu^*K$ of a knot $K\subset S^3$ can be displaced from the zero section $0_{S^3}$ in $T^*S^3.$ Having no intuition about whether/how often this happens in general, I am opening up a discussion on the following question:
Are there any concrete statements on, given a closed submanifold $N$ in a closed manifold $M,$ when is the conormal bundle $\nu^*N$ displaceable from the zero section $0_M$ in the cotangent bundle $T^*M$?
Any result possibly involving some conditions on $M$ and $N$, or any particular case of $M$ and $N$ when the answer is known, would be appreciated. Thanks!
