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The \(\nu ^+\)-equivalence classes of genus one knots

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Abstract

The \(\nu ^+\)-equivalence is an equivalence relation on the knot concordance group. This relation can be seen as a certain stable equivalence on knot Floer complexes \(CFK^{\infty }\), and many concordance invariants derived from Heegaard Floer theory are invariant under the relation. In this paper, we show that any genus one knot is \(\nu ^+\)-equivalent to one of the trefoil, its mirror and the unknot.

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Acknowledgements

The authors would like to thank Jennifer Hom, Min Hoon Kim and JungHwan Park for many interesting conversations about the present work. The author was supported by JSPS KAKENHI Grant Number 18J00808.

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  1. Meijo University, Nagoya, Japan

    Kouki Sato

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  1. Kouki Sato
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Correspondence to Kouki Sato.

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Sato, K. The \(\nu ^+\)-equivalence classes of genus one knots. Sel. Math. New Ser. 29, 63 (2023). https://doi.org/10.1007/s00029-023-00867-6

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