Geodesic
Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials
Canadian journal of mathematics, Tome 74 (2022) no. 4, pp. 1137-1176

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DOI

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.
DOI : 10.4153/S0008414X21000183
Mots-clés : Ribbon concordance, Seifert form, Blanchfield pairing, twisted Alexander polynomial, Levine–Tristram signatures 
Friedl, Stefan; Kitayama, Takahiro; Lewark, Lukas; Nagel, Matthias; Powell, Mark. Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials. Canadian journal of mathematics, Tome 74 (2022) no. 4, pp. 1137-1176. doi: 10.4153/S0008414X21000183
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     author = {Friedl, Stefan and Kitayama, Takahiro and Lewark, Lukas and Nagel, Matthias and Powell, Mark},
     title = {Homotopy ribbon concordance, {Blanchfield} pairings, and twisted {Alexander} polynomials},
     journal = {Canadian journal of mathematics},
     pages = {1137--1176},
     year = {2022},
     volume = {74},
     number = {4},
     doi = {10.4153/S0008414X21000183},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X21000183/}
}
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