English

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

R2 v1 2026-06-23T18:05:34.717Z