Boundary slope diameter and crossing number of 2-bridge knots

Abstract

We prove that for 2-bridge knots, the diameter, D, of the set of boundary slopes is twice the crossing number, c. This constitutes partial verification of a conjecture that, for all knots in S^3, D is at most 2c.

arXiv comment21 pages, 7 figures. v2 - No changes - we only wish to note that this is an early version of a paper to appear in The Osaka Journal of Mathematics

References in corpus (1)

• Crossing number and diameter of boundary slope set of Montesinos knot

Cited by in corpus (1)

• The Jones polynomial and boundary slopes of alternating knots