Search

We establish homotopy ribbon concordance obstructions coming from the Blanchfield form and Levine–Tristram signatures. Then, as an application of twisted Alexander polynomials, we show that for every knot K with nontrivial Alexander polynomial, there exists an infinite family of knots that are all concordant to K and have the same Blanchfield form as K, such that no pair of knots in that family is homotopy ribbon concordant.

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 $\text{Bl(}L\text{)}$.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials

An Explicit Computation of the Blanchfield Pairing for Arbitrary Links

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials

An Explicit Computation of the Blanchfield Pairing for Arbitrary Links