TY - JOUR

T1 - Two-bridge knots with unknotting number one

AU - Kanenobu, Taizo

AU - Murakami, Hitoshi

PY - 1986/11

Y1 - 1986/11

N2 - 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.

AB - 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.

KW - Dehn surgery

KW - Lens space

KW - Two-bridge knot

KW - Unknotting number

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U2 - 10.1090/S0002-9939-1986-0857949-8

DO - 10.1090/S0002-9939-1986-0857949-8

M3 - Article

AN - SCOPUS:84968505712

SN - 0002-9939

VL - 98

SP - 499

EP - 502

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 3

ER -