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Journal Article

Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials

MPS-Authors
/persons/resource/persons235267

Friedl,  Stefan
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons285321

Kitayama,  Takahiro
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons235692

Lewark,  Lukas
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons267362

Nagel,  Matthias       
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons236018

Powell,  Mark
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://arxiv.org/abs/2007.15289
(Preprint)

https://doi.org/10.4153/S0008414X21000183
(Publisher version)

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Citation

Friedl, S., Kitayama, T., Lewark, L., Nagel, M., & Powell, M. (2022). Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials. Canadian Journal of Mathematics, 74(4), 1137-1176. doi:10.4153/S0008414X21000183.


Cite as: https://hdl.handle.net/21.11116/0000-000C-3FA4-5
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.