Communications of the
Korean Mathematical Society CKMS

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Commun. Korean Math. Soc. 2020; 35(3): 1037-1043

Online first article January 22, 2020      Printed July 31, 2020

https://doi.org/10.4134/CKMS.c190329

Copyright © The Korean Mathematical Society.

Algebraically concordant Seifert forms and knot concordance

Taehee Kim

Konkuk University

Abstract

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We show that if $M$ and $V$ are Seifert forms such that $M$ is metabolic and has nontrivial Alexander polynomial, then there exists a knot $K$ having Seifert form $M\oplus V$ that is not concordant to any knot with Seifert form $V$.

Keywords: Concordance, Seifert forms, von-Neumann $\rhot$-invariants

MSC numbers: Primary 57N70, 57M25

Supported by: This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (no. 2018R1D1A1 B07048361)

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