A calculation of Blanchfield pairings of 3-manifolds and knots

Abstract

We calculate Blanchfield pairings of 3-manifolds. In particular, we give a formula for the Blanchfield pairing of a fibred 3-manifold and we give a new proof that the Blanchfield pairing of a knot can be expressed in terms of a Seifert matrix.

17 pages. For version 2, we have generalised from knot exteriors to generic 3-manifolds with a map to the circle, included an explicit formula for the Blanchfield pairing of a fibred 3-manifold in terms of the monodromy, and indicated how to obtain a derivation of the analogous formula for the Blanchfield pairing of a high dimensional knot