Repeated boundary slopes for 2-bridge knots
Cynthia L. Curtis, William Franczak, Randolph J. Leiser, Ryan J., Manheimer
TL;DR
This paper explores when different branched surfaces in 2-bridge knot complements support essential surfaces sharing the same boundary slope, identifying all such cases and an infinite family with no repeated slopes.
Contribution
It provides a complete classification of boundary slope repetitions in 2-bridge knots and introduces an infinite family with unique boundary slopes.
Findings
All instances of repeated boundary slopes are characterized.
An infinite family of 2-bridge knots with no repeated boundary slopes is identified.
The results clarify the relationship between branched surfaces and boundary slopes in knot complements.
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.
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