Abstract

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

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