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A note on thickness of knots

### András I. Stipsicz and Zoltán Szabó

Vol. 5 (2022), No. 1, 299–308
##### Abstract

We introduce a numerical invariant $\beta \left(K\right)\in ℕ\cup \left\{0\right\}$ of a knot $K\subset {S}^{3}$ which measures how nonalternating $K$ is. We prove an inequality between $\beta \left(K\right)$ and the (knot Floer) thickness $\left(K\right)$ of a knot $K$. As an application we show that all Montesinos knots have thickness at most one.

##### Keywords
knot Floer homology, thickness, alternating knots
Primary: 57K10
##### Milestones
Received: 17 January 2021
Revised: 22 February 2021
Accepted: 28 April 2021
Published: 27 October 2022
##### Authors
 András I. Stipsicz Rényi Institute of Mathematics Budapest Hungary Zoltán Szabó Department of Mathematics Princeton University Princeton, NJ United States