Computation of the knot Floer complex of knots of thickness one

TL;DR

This paper introduces an algorithm to compute the knot Floer complex for knots of thickness one and extends it to analyze Dehn surgeries, revealing characterizing slopes for knots with up to 17 crossings.

Contribution

The paper presents a novel algorithm for computing the full knot Floer complex of knots of thickness one and applies it to identify characterizing slopes in Dehn surgeries.

Findings

Algorithm successfully computes knot Floer complexes for knots of thickness one.

Extended algorithm helps identify characterizing slopes for most knots with up to 17 crossings.

Most non-integral Dehn surgery slopes are shown to be characterizing for these knots.

Abstract

We develop and implement an algorithm that computes the full knot Floer complex of knots of thickness one. As an application, by extending this algorithm to certain knots of thickness two, we show that all but finitely many non-integral Dehn surgery slopes are characterizing for most knots with up to 17 crossings.