Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials

Stefan Friedl; Takahiro Kitayama; Lukas Lewark; Matthias Nagel; Mark Powell

doi:10.4153/s0008414x21000183

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arXiv · 2007.15289

Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials

Stefan Friedl·Takahiro Kitayama·Lukas Lewark·Matthias Nagel·Mark Powell

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Abstract

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.

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Stefan Friedl, Takahiro Kitayama, Lukas Lewark, Matthias Nagel, Mark Powell. 2020-07-30. Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials. https://doi.org/10.4153/s0008414x21000183

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