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

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 $CF{K}^{\mathrm{\infty }}$, 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.