The v+-equivalence classes of genus one knots

• Kouki Sato ^[1]
  1. [1] Meijo University

     Meijo University

     Naka-ku, Japón

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 4, 2023
• Idioma: inglés
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• Resumen

  • The ν+-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 ∞, 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 ν+-equivalent to one of the trefoil, its mirror and the unknot.