A Counterexample to the Bernhard–Jablan Unknotting Conjecture. Issue 4 (1st December 2021)

• Record Type: Journal Article
• Authors: Brittenham, Mark; Hermiller, Susan
• Is Part Of: Experimental mathematics. Volume 30:Issue 4(2021)
• Page Start: 547
• Page End: 556
• Publication Date: 2021-12-01
• Subjects: Unknotting number -- minimal crossing diagram -- SnapPy -- Knotscape; 57M27 -- 57M25; Mathematics -- Periodicals; Mathematics -- Research -- Periodicals; 510.724
• DOI: 10.1080/10586458.2019.1580633
• Languages: English
• ISSNs: 1058-6458

Abstract

Abstract: We show that there is a knot satisfying the property that for each minimal crossing number diagram of the knot and each single crossing of the diagram, changing the crossing results in a diagram for a knot whose unknotting number is at least that of the original knot, thus giving a counterexample to the Bernhard–Jablan Conjecture.