Crosscap number and knot projections
Geometric Topology
2020-08-26 v1
Abstract
We introduce an unknotting-type number of knot projections that gives an upper bound of the crosscap number of knots. We determine the set of knot projections with the unknotting-type number at most two, and this result implies classical and new results that determine the set of alternating knots with the crosscap number at most two.
Keywords
Cite
@article{arxiv.2008.11061,
title = {Crosscap number and knot projections},
author = {Noboru Ito and Yusuke Takimura},
journal= {arXiv preprint arXiv:2008.11061},
year = {2020}
}
Comments
20 pages, 20 figures