Smooth concordance of cables of the figure-eight knot

2025/05/06 by Sungkyung Kang, Kang, Sungkyung, JungHwan Park +3 · 1 citation
Engineering · Biochemistry, Genetics and Molecular Biology · #Metal Forming Simulation Techniques #Congenital limb and hand anomalies

paper · pdf · doi:10.48550/arxiv.2505.03720

Abstract

We prove that every nontrivial cable of the figure-eight knot has infinite order in the smooth knot concordance group. Our main contribution is a uniform proof that applies to all (2n,1)-cables of the figure-eight knot. To this end, we introduce a family of concordance invariants κ_R^(k), defined via 2^k-fold branched covers and real Seiberg--Witten Floer K-theory. These invariants generalize the real K-theoretic Frøyshov invariant developed by Konno, Miyazawa, and Taniguchi.

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