The Jones polynomial and boundary slopes of alternating knots

Cynthia L. Curtis; Samuel Taylor

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arXiv · 0910.4912

The Jones polynomial and boundary slopes of alternating knots

Cynthia L. Curtis·Samuel Taylor

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Abstract

We show for an alternating knot the minimal boundary slope of an essential spanning surface is given by the signature plus twice the minimum degree of the Jones polynomial and the maximal boundary slope of an essential spanning surface is given by the signature plus twice the maximum degree of the Jones polynomial. For alternating Montesinos knots, these are the minimal and maximal boundary slopes.

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BibTeX RIS

Cynthia L. Curtis, Samuel Taylor. 2014-01-13. The Jones polynomial and boundary slopes of alternating knots. https://arxiv.org/abs/0910.4912

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