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

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.

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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.

Item Type:
Other
Additional Information:
I helped author the appendix to this article, “A note on Wirtinger number and flypes,” rather than the main article. My name therefore appears above the appendix instead of in the main author line.
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2614
Subjects:
ID Code:
147938
Deposited By:
Deposited On:
07 Oct 2020 09:20
Refereed?:
No
Published?:
Published
Last Modified:
28 Oct 2020 09:23