Document Type
Article - post-print
Publication Date
2019
Abstract
A partial order on prime knots can be defined by declaring π½β₯πΎ, if there exists an epimorphism from the knot group of π½ onto the knot group of πΎ. Suppose that π½ is a 2-bridge knot that is strictly greater than π distinct, nontrivial knots. In this paper, we determine a lower bound on the crossing number of π½ in terms of π. Using this bound, we answer a question of Suzuki regarding the 2-bridge epimorphism number EK(π) which is the maximum number of nontrivial knots which are strictly smaller than some 2-bridge knot with crossing number π. We establish our results using techniques associated with parsings of a continued fraction expansion of the defining fraction of a 2-bridge knot.
Recommended Citation
Hoste, Jim, et al. βRemarks on Suzukiβs Knot Epimorphism Number.β Journal of Knot Theory and Its Ramifications, vol. 28, no. 09, Aug. 2019. doi:10.1142/S0218216519500603.
