A note on thickness of knots

TL;DR

This paper introduces a new numerical invariant for knots that quantifies their non-alternating nature and relates it to knot Floer thickness, with applications to Montesinos knots.

Contribution

It defines the invariant (K) and establishes an inequality linking it to knot Floer thickness, providing new insights into knot classification.

Findings

(K) measures non-alternating complexity

Inequality between (K) and Floer thickness is proven

Montesinos knots have Floer thickness at most one

Abstract

We introduce a numerical invariant \beta(K) of a knot K which measures how non-alternating K is. We prove an inequality between \beta (K) and the (knot Floer) thickness of K. As an application we show that all Montesinos knots have thickness at most one.