In this archiv paper which is continuation of following:
authors prove that manifold $M$ codimension 2 bounds so called Seifert surface of codimension 1 when manifold $M$ normal bundle is trivial. Consider now 3-manifold $M$ embedded in 5-dimensional Euclidean space having trivial normal bundle. Let $N_1$ be 4-manifold which boundary is $M$ according to above work. I would like to consider $M$ which is not knotted. For the moment let's consider following definition. $M$ embedded in 5-space is not knotted when exist closed 4-manifold $N$ embracing $M$ and $M$ separates $N$. This "definition" is wrong - see comments below from Danny Rubermann.
This is just work definition, because for giving embedded $M$ I would like to construct such $N$.
My next step is to see whether I can make $N$ 1-connected. If yes then let's look at second homotopy or homology of $N$. I saw somewhere statement that in such case $\pi_2=H_2$ has no torsion - I cannot find it now here. Now we look at Mayer-Vietoris to see what possibilities for $N, N_1, N_2$ are for given $H_1M$. The plan is to find simplest possible $N$. If $N$ is sphere then it means that $M$ is embeddable in 4-space. Otherwise - if we cannot make $N$ sphere then $M$ is not embeddable in 4-space.
Does this plan make sense ?