Geodesic
An Explicit Computation of the Blanchfield Pairing for Arbitrary Links
Canadian journal of mathematics, Tome 70 (2018) no. 5, pp. 983-1007

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DOI

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 $\text{Bl(}L\text{)}$ .
DOI : 10.4153/CJM-2017-051-5
Mots-clés : 57M25, link, Blanchfield pairing, C-complex, Alexander module 
Conway, Anthony. An Explicit Computation of the Blanchfield Pairing for Arbitrary Links. Canadian journal of mathematics, Tome 70 (2018) no. 5, pp. 983-1007. doi: 10.4153/CJM-2017-051-5
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     title = {An {Explicit} {Computation} of the {Blanchfield} {Pairing} for {Arbitrary} {Links}},
     journal = {Canadian journal of mathematics},
     pages = {983--1007},
     year = {2018},
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     doi = {10.4153/CJM-2017-051-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2017-051-5/}
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