Tait's conjectures and odd crossing number amphicheiral knots

Details Tait's conjectures and odd crossing number amphicheiral knots Tait's conjectures and odd crossing number amphicheiral knots

2007-04-16

arxiv.org/abs/0704.1941v1

Bull. Amer. Math. Soc. 45 (2008), 285--291.

Mathematics

Geometric Topology

5 pages, 1 figure; this is an elementarily written research announcement; some/full account is/will be given in (a revision of

Scientific paper

We give a brief historical overview of the Tait conjectures, made 120 years ago in the course of his pioneering work in tabulating the simplest knots, and solved a century later using the Jones polynomial. We announce the solution, again based on a substantial study of the Jones polynomial, of one (possibly his last remaining?) problem of Tait, with the construction of amphicheiral knots of almost all odd crossing numbers. An application to the non-triviality problem for the Jones polynomial is also outlined.

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