The almost alternating diagrams of the trivial knot

The almost alternating diagrams of the trivial knot

Bankwitz characterized the alternating diagrams of the trivial knot. A non-alternating diagram is called almost alternating if one crossing change makes the diagram alternating. We characterize the almost alternating diagrams of the trivial knot. As a corollary, we determine the unknotting number on...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of topology 2009, Vol.2 (1), p.77-104
1. Verfasser: Tsukamoto, Tatsuya
Format: Artikel
Sprache:eng
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Bankwitz characterized the alternating diagrams of the trivial knot. A non-alternating diagram is called almost alternating if one crossing change makes the diagram alternating. We characterize the almost alternating diagrams of the trivial knot. As a corollary, we determine the unknotting number one alternating knots with the property that the unknotting operation can be done on its alternating diagram.
ISSN:1753-8416
1753-8424
DOI:10.1112/jtopol/jtp001