An Explicit Computation of the Blanchfield Pairing for Arbitrary Links

Conway, Anthony

Canadian journal of mathematics, Tome 70 (2018) no. 5, pp. 983-1007

Résumé

Given a link $L$ , the Blanchfield pairing $\text{Bl(}L\text{)}$ is a pairing that 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, $\text{Bl(}L\text{)}$ 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 $\text{Bl(}L\text{)}$ .

Détail

DOI : 10.4153/CJM-2017-051-5

Mots-clés : 57M25, link, Blanchfield pairing, C-complex, Alexander module

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