Let be a tame knot with irreducible exterior in a closed, connected, orientable 3–manifold such that is cyclic. If is not a strict boundary slope, then the diameter of the set of strict boundary slopes of , denoted , is a numerical invariant of . We show that either (i) or (ii) 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.
"The diameter of the set of boundary slopes of a knot." Algebr. Geom. Topol. 6 (3) 1095 - 1112, 2006. https://doi.org/10.2140/agt.2006.6.1095