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An Explicit Computation of the Blanchfield Pairing for Arbitrary Links
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- Journal:
- Canadian Journal of Mathematics / Volume 70 / Issue 5 / 01 October 2018
- Published online by Cambridge University Press:
- 20 November 2018, pp. 983-1007
- Print publication:
- 01 October 2018
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- Article
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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 $\text{Bl(}L\text{)}$.
