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

46 pages, 8 figures;(v2)typos corrected

References in corpus (2)

• Knot Floer homology detects fibred knots
• A full-twist inequality for the ${\nu }^{+}$-invariant

Cited by in corpus (2)

• Instantons, special cycles, and knot concordance
• One-bipolar topologically slice knots and primary decomposition