Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials
arXiv:2007.15289 · doi:10.4153/S0008414X21000183
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.
arXiv comment33 pages. Comments welcome. v2: Added details and new Example 3.5, accepted for publication by Canadian Journal of Mathematics
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