Slicing degree of knots

2024/04/24 by Qianhe Qin, Qin, Qianhe
Computer Science · Mathematics · #57K10 #57K18 #57K40 #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2404.15991

openalex publication_date 2024/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The slicing degree of a knot K is defined as the smallest integer k such that K is k-slice in #ⁿ \mathbbCP² 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.

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