A full-twist inequality for the ${\nu }^{+}$-invariant

Abstract

Hom and Wu introduced a knot concordance invariant called ${\nu }^{+}$, which dominates many concordance invariants derived from Heegaard Floer homology. In this paper, we give a full-twist inequality for ${\nu }^{+}$. By using the inequality, we extend Wu's cabling formula for ${\nu }^{+}$ (which is proved only for particular positive cables) to all cables in the form of an inequality. In addition, we also discuss ${\nu }^{+}$-equivalence, which is an equivalence relation on the knot concordance group. We introduce a partial order on ${\nu }^{+}$-equivalence classes, and study its relationship to full-twists.

17 pages, 11 figures

References in corpus (1)

• On the Khovanov and knot Floer homologies of quasi-alternating links

Cited by in corpus (3)

• The ${\nu }^{+}$-equivalence classes of genus one knots
• One-bipolar topologically slice knots and primary decomposition
• On eigenvalues of double branched covers