Crosscap number and knot projections
arXiv:2008.11061 · doi:10.1142/S0129167X18500842
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.
20 pages, 20 figures