Polynomial values, the linking form and unknotting numbers

Details Polynomial values, the linking form and unknotting numbers Polynomial values, the linking form and unknotting numbers

2004-05-05

arxiv.org/abs/math/0405076v1

Math. Res. Lett. 11(5-6) (2004), 755--769.

Mathematics

Geometric Topology

10 pages

Scientific paper

We show how the signed evaluations of link polynomials can be used to calculate unknotting numbers. We use the Jones-Rong value of the Brandt-Lickorish-Millett-Ho polynomial Q to calculate the unknotting numbers of 8_{16}, 9_{49} and 6 further new entries in Kawauchi's tables. Another method is developed by applying and extending the linking form criterion of Lickorish. This leads to several conjectured relations between the Jones value of Q and the linking form.

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