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.
ASJC Scopus subject areas
- 数学 (全般)