The Jones polynomial and boundary slopes of alternating knots

Details The Jones polynomial and boundary slopes of alternating knots The Jones polynomial and boundary slopes of alternating knots

2009-10-26

arxiv.org/abs/0910.4912v2

Mathematics

Geometric Topology

8 pages, 4 figures

Scientific paper

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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