An explicit computation of the Blanchfield pairing for arbitrary links
Abstract
Given a link $L$, the Blanchfield pairing $\operatorname{Bl}(L)$ is a pairing which is defined on the torsion submodule of the Alexander module of $L$. In some particular cases, namely if $L$ is a boundary link or if the Alexander module of $L$ is torsion, $\operatorname{Bl}(L)$ can be computed explicitly; however no formula is known in general. In this article, we compute the Blanchfield pairing of any link, generalizing the aforementioned results. As a corollary, we obtain a new proof that the Blanchfield pairing is hermitian. Finally, we also obtain short proofs of several properties of $\operatorname{Bl}(L)$.
 Publication:

arXiv eprints
 Pub Date:
 June 2017
 arXiv:
 arXiv:1706.00226
 Bibcode:
 2017arXiv170600226C
 Keywords:

 Mathematics  Geometric Topology
 EPrint:
 23 pages, 1 figure. v2: Corollary 1.2 has been weakened