Crosscap numbers and the Jones polynomial
Geometric Topology
2016-04-19 v3
Abstract
We give sharp two-sided linear bounds of the crosscap number (non-orientable genus) of alternating links in terms of their Jones polynomial. Our estimates are often exact and we use them to calculate the crosscap numbers for several infinite families of alternating links and for several alternating knots with up to twelve crossings. We also discuss generalizations of our results for classes of non-alternating links.
Cite
@article{arxiv.1408.4493,
title = {Crosscap numbers and the Jones polynomial},
author = {Efstratia Kalfagianni and Christine Ruey Shan Lee},
journal= {arXiv preprint arXiv:1408.4493},
year = {2016}
}
Comments
27 pages. Minor corrections and modifications. To appear in Advances of Mathematics