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The skein polynomial of closed 3-braids

A. Stoimenow
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Abstract

Using the band representation of the 3-strand braid group, it is shown that the genus of 3-braid links can be read off their skein polynomial. Some applications are given, in particular a simple proof of Morton's conjectured inequality and a condition to decide that some polynomials, like the one of 9_{49}, are not admitted by 3-braid links. Finally, alternating links of braid index 3 are classified.

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A. Stoimenow. 2001-04-01. The skein polynomial of closed 3-braids. https://arxiv.org/abs/math/0103041

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