Two-bridge knots with unknotting number one

Taizo Kanenobu, Hitoshi Murakami

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)

Abstract

We determine all two-bridge knots with unknotting number one. In fact we prove that a two-bridge knot has unknotting number one iff there exist positive integers p, m, and n such that (m, n) = 1 and Imn = p ±1, and it is equivalent to S(p, 2n2) in Schubert's notation. It is also shown that it can be expressed as C(a, a1, a2,…, ak, ±2,—ak,…,—a2,—a1) using Conway's notation.

Original languageEnglish
Pages (from-to)499-502
Number of pages4
JournalProceedings of the American Mathematical Society
Volume98
Issue number3
DOIs
Publication statusPublished - 1986 Nov
Externally publishedYes

Keywords

  • Dehn surgery
  • Lens space
  • Two-bridge knot
  • Unknotting number

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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