Blanchfield and Seifert algebra in high-dimensional knot theory

The Blanchfield and Seifert forms of knot theory have algebraic analogues over arbitrary rings with involution. The covering Blanchfield form of a Seifert form is an algebraic analogue of the expression of the infinite cyclic cover of a knot complement as the infinite union of copies of a cobordism between two copies of a Seifert surface. The inverse construction of the Seifert forms of a Blanchfield form is an algebraic analogue of the transversality construction of the Seifert surfaces of a knot as codimension 1 submanifolds of the knot complement.