Unknotting numbers of diagrams of a given nontrivial knot are unbounded

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We show that for any nontrivial knot K and any natural number n, there is a diagram D of K such that the unknotting number of D is greater than or equal to n. It is well-known that twice the unknotting number of K is less than or equal to the crossing number of K minus one. We show that the equality holds only when K is a (2, p)-torus knot.

Original languageEnglish
Pages (from-to)1049-1063
Number of pages15
JournalJournal of Knot Theory and its Ramifications
Volume18
Issue number8
DOIs
Publication statusPublished - 2009 Aug 1

Keywords

  • Crossing number.
  • Knot
  • Unknotting number
  • Unknotting number of diagram

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'Unknotting numbers of diagrams of a given nontrivial knot are unbounded'. Together they form a unique fingerprint.

  • Cite this