A note on knot Floer thickness and the dealternating number

TL;DR

This paper provides a concise proof that knot Floer thickness serves as a lower bound for the dealternating number of a knot, refining previous results with a modified approach.

Contribution

It offers a simplified proof connecting knot Floer thickness to the dealternating number using Kauffman states and bad domains.

Findings

Knot Floer thickness bounds the dealternating number.

The proof adapts the Stipsicz-Szabo approach.

Thickness relates to minimal bad domains in diagrams.

Abstract

In this note, we give a short proof that knot Floer thickness is a lower bound on the dealternating number of a knot. The result is originally due to work of Abe and Kishimoto, Lowrance, and Turaev. Our proof is a modification of the Stipsicz-Szabo approach using Kauffman states to show that thickness bounds the minimal number of bad domains in a knot diagram.