Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials

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

• Item Type: Articles
• Additional Information: S.F. was supported by the SFB 1085 “higher invariants”, funded by the DFG. T.K. was supported by JSPS KAKENHI Grant Numbers JP18K13404, JP18KK0380. L.L. was supported by the Emmy Noether Program of the DFG. M.N. gratefully acknowledges support by the SNSF Grant 181199.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Powell, Professor Mark
• Authors: Friedl, S., Kitayama, T., Lewark, L., Nagel, M., and Powell, M.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Canadian Journal of Mathematics
• Publisher: Cambridge University Press
• ISSN: 0008-414X
• ISSN (Online): 1496-4279
• Published Online: 12 April 2021
• Copyright Holders: Copyright © Canadian Mathematical Society 2021
• First Published: First published in Canadian Journal of Mathematics 74(4): 1137-1176
• Publisher Policy: Reproduced in accordance with the publisher copyright policy