2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227776Let K be a tame knot with irreducible exterior M(K) in a closed, connected, orientable 3--manifold Sigma such that pi_1(Sigma) is cyclic. If infinity is not a strict boundary slope, then the diameter of the set of strict boundary slopes of K, denoted d_K, is a numerical invariant of K. We show that either (i) d_K >= 2 or (ii) K is a generalized iterated torus knot. The proof combines results from Culler and Shalen [Comment. Math. Helv. 74 (1999) 530-547] with a result about the effect of cabling on boundary slopes.This is the version published by Algebraic & Geometric Topology on 29 August 2006Geometric Topology57M15, 57M25, 57M50text