  We study the cobordism of manifolds with boundary, and its applications to
codimension 2 embeddings $M^m\subset N^{m+2}$, using the method of the
algebraic theory of surgery. The first main result is a splitting theorem for
cobordisms of algebraic Poincar\'e pairs, which is then applied to describe the
behaviour on the chain level of Seifert surfaces of embeddings $M^{2n-1}
\subset S^{2n+1}$ under isotopy and cobordism. The second main result (update:
which is false) is that the $S$-equivalence class of a Seifert form is an
isotopy invariant of the embedding, generalizing the Murasugi--Levine result
for knots and links. The third main result is a generalized Murasugi--Kawauchi
inequality giving an upper bound on the difference of the Levine--Tristram
signatures of cobordant embeddings.
