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

Kouki Sato

doi:10.1007/s00029-023-00867-6

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arXiv · 1907.09116

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

Kouki Sato

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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 equivalence. 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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Kouki Sato. 2019-07-22. The $\nu^+$-equivalence classes of genus one knots. https://doi.org/10.1007/s00029-023-00867-6

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