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

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.