Twisted cohomology pairings of knots II; to some Blanchfield pairings

Abstract

In this paper, we study some comparison between a bilinear cohomology pairing in local coefficients and the Blanchfield pairing of a knot. We show that the former pairing is an [Formula: see text]-equivalent invariant, and give a criterion to a relation between the two pairings. We also observe that the pairings of some knots are equivalent, and that the pairings of other knots are not equivalent.