Twisted cohomology pairings of knots I; diagrammatic computation

Abstract

We provide a diagrammatic computation for the bilinear form, which is defined as the pairing between the (relative) cup products with every local coefficients and every integral homology 2-class of every links in the 3-sphere. As a corollary, we construct bilinear forms on the twisted Alexander modules of links.

arXiv commentAny comments are welcome. 23 pages and 5 figures. I divided a certain preprint into some parts. This paper is the first one. Furthermore, in this second version, I rewrote Sections 2,3,4 to make them more understable

Cited by in corpus (2)

• Bilinear-form invariants of Lefschetz fibrations over the 2-sphere
• Some comparisons of Blanchfield pairings and cohomology pairings of knots