An Explicit Computation of the Blanchfield Pairing for Arbitrary Links

  title={An Explicit Computation of the Blanchfield Pairing for Arbitrary Links},
  author={Anthony Conway},
  journal={Canadian Journal of Mathematics},
  pages={983 - 1007}
  • Anthony Conway
  • Published 1 June 2017
  • Mathematics
  • Canadian Journal of Mathematics
Abstract 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… 
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