On a conjecture of K. Murasugi

William Schumacher Massey and Lorenzo Traldi

Vol. 124 (1986), No. 1, 193–213

DOI: 10.2140/pjm.1986.124.193

Abstract

K. Murasugi has conjectured that if every pair of the μ components of a classical link L has linking number ±1, then the group G of L will have the property that G_q∕G_q+1≅F_q∕F_q+1 ∀q ≥ 2, where F is free on μ − 1 generators. (The conjecture has been verified by other authors.) Here we show that this property is equivalent to the special case G₂∕G₃≅F₂∕F₃, and also give other equivalent conditions.

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 20F14

Milestones

Received: 10 March 1985

Published: 1 September 1986