Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials
Geometric Topology
2022-09-05 v2
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.
Keywords
Cite
@article{arxiv.2007.15289,
title = {Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials},
author = {Stefan Friedl and Takahiro Kitayama and Lukas Lewark and Matthias Nagel and Mark Powell},
journal= {arXiv preprint arXiv:2007.15289},
year = {2022}
}
Comments
33 pages. Comments welcome. v2: Added details and new Example 3.5, accepted for publication by Canadian Journal of Mathematics