Say let $M$ be an codimension 2 submanifold of $N$, when do we have $M=M_1\cap M_2$, s.t. $M_i$ are codimension 1 submanifold intersecting transversally?
My guess is if $M$ is a knot and $N=S^3$, this condition do not holds. do we have a characterization for this?