Crosscap numbers of pretzel knots
Geometric Topology
2007-05-23 v2
Abstract
The crosscap number of a knot in the 3-sphere is defined as the minimal first Betti number of non-orientable subsurfaces bounded by the knot. In this paper, we determine the crosscap numbers of pretzel knots. The key ingredient to obtain the result is the algorithm of enumerating all essential surfaces for Montesinos knots developed by Hatcher and Oertel.
Cite
@article{arxiv.math/0608480,
title = {Crosscap numbers of pretzel knots},
author = {Kazuhiro Ichihara and Shigeru Mizushima},
journal= {arXiv preprint arXiv:math/0608480},
year = {2007}
}
Comments
13 pages, 10 figures, v2: An assumption of the main theorem is clarified