Tait's conjectures and odd crossing number amphicheiral knots
Geometric Topology
2008-08-30 v1 History and Overview
Abstract
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.
Cite
@article{arxiv.0704.1941,
title = {Tait's conjectures and odd crossing number amphicheiral knots},
author = {A. Stoimenow},
journal= {arXiv preprint arXiv:0704.1941},
year = {2008}
}
Comments
5 pages, 1 figure; this is an elementarily written research announcement; some/full account is/will be given in (a revision of) math/0606255