Blair, Ryan and Ozawa, Makoto and Kjuchukova, Alexandra and Morrison, Nathaniel (2019) The incompatibility of crossing number and bridge number for knot diagrams Appendix. A note on Wirtinger number and flypes by Ryan Blair and Nathaniel Morrison. Elsevier.
Full text not available from this repository.Abstract
We study methods for computing the bridge number of a knot from a knot diagram. We prove equivalence between a geometric and a combinatorial definition of the bridge number of a knot diagram. For each notion of diagrammatic bridge number considered, we find crossing number minimizing knot diagrams which fail to minimize bridge number. Furthermore, we construct a family of minimal crossing diagrams for which the difference between diagrammatic bridge number and the actual bridge number of the knot grows to infinity.