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arXiv · 1706.02820

A full-twist inequality for the $ν^+$-invariant

Kouki Sato
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Abstract

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

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Kouki Sato. 2017-06-09. A full-twist inequality for the $ν^+$-invariant. https://doi.org/10.1016/j.topol.2018.06.010

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