Repeated boundary slopes for 2-bridge knots

Abstract

We investigate the question of when distinct branched surfaces in the complement of a 2-bridge knot support essential surfaces with identical boundary slopes. We determine all instances in which this occurs and identify an infinite family of knots for which no boundary slopes are repeated.

State invariants of 2-bridge knots

“…To prove the theorem, we identify knots with continued fraction expansions of the appropriate lengths. See for example the algorithm of Proposition 3.3 of [6] for identifying the continued fraction expansions for a knot K.…”