Some families of minimal elements for the partial ordering on prime knots
Geometric Topology
2014-09-03 v2
Abstract
We show that all twist knots, certain double twist knots and some other 2-bridge knots are minimal elements for the partial ordering on the set of prime knots. The key to these results are presentations of their character varieties using Chebyshev polynomials and a criterion for irreducibility of a polynomial of two variables. These give us an elementary method to discuss the number of irreducible components of the character varieties, which concludes the result essentially.
Keywords
Cite
@article{arxiv.1301.0138,
title = {Some families of minimal elements for the partial ordering on prime knots},
author = {Fumikazu Nagasato and Anh T. Tran},
journal= {arXiv preprint arXiv:1301.0138},
year = {2014}
}
Comments
Title changed, 12 pages