Slicing degree of knots

Abstract

The slicing degree of a knot $K$ is defined as the smallest integer $k$ such that $K$ is $k$-slice in ${\#}^n\overline{{\mathbb{CP}}^2}$ for some $n$. In this paper, we establish bounds for the slicing degrees of knots using Rasmussen's $s$-invariant, knot Floer homology and singular instanton homology. We compute the slicing degrees for many small knots (with crossing numbers up to $9$) and for some families of torus knots.

arXiv comment17 pages, 2 figures