Cobordisms of immersions with codimension two

We single out the obstruction for a closed $\mathbb Z_2$-null homologous submanifold of codimension 2 to be the boundary of a submanifold of codimension 1. As an application, we calculate the groups $E\mathscr N_n(\mathbb R^{n+2})$ of cobordisms of embeddings of nonoriented $n$-manifolds in the Euclidean $n+2$-space for $n=3$ and 4. Namely, we show that $E\mathscr N_3(\mathbb R^2)=\mathbb Z_2$, $E\mathscr N_4(\mathbb R^6)=0$. A specific generator of the former group is explicitly given.