Bounds on the Crosscap Number of Torus Knots
Geometric Topology
2007-05-23 v2
Abstract
For a torus knot K, we bound the crosscap number c(K) in terms of the genus g(K) and crossing number n(K): c(K) \leq [(g(K)+9)/6] and c(K) \leq [(n(K) + 16)/12]. The (6n-2,3) torus knots show that these bounds are sharp.
Keywords
Cite
@article{arxiv.math/0409581,
title = {Bounds on the Crosscap Number of Torus Knots},
author = {Thomas W. Mattman and Owen Sizemore},
journal= {arXiv preprint arXiv:math/0409581},
year = {2007}
}
Comments
7 Pages, 0 figures Version 2 - corrected a typo: Clark showed c(K) \le 2g(K) + 1