Blanchfield and Seifert algebra in high dimensional knot theory

Abstract

Novikov initiated the study of the algebraic properties of quadratic forms over polynomial extensions by a far-reaching analogue of the Pontrjagin-Thom transversality construction of a Seifert surface of a knot and the infinite cyclic cover of the knot exterior. In this paper the analogy is applied to explain the relationship between the Seifert forms over a ring with involution and Blanchfield forms over the Laurent polynomial extension.