Document Type
Article - post-print
Publication Date
2019
Abstract
A partial order on prime knots can be defined by declaring ��≥��, if there exists an epimorphism from the knot group of �� onto the knot group of ��. Suppose that �� is a 2-bridge knot that is strictly greater than �� distinct, nontrivial knots. In this paper, we determine a lower bound on the crossing number of �� in terms of ��. Using this bound, we answer a question of Suzuki regarding the 2-bridge epimorphism number EK(��) which is the maximum number of nontrivial knots which are strictly smaller than some 2-bridge knot with crossing number ��. We establish our results using techniques associated with parsings of a continued fraction expansion of the defining fraction of a 2-bridge knot.
Original Publication Citation
Hoste, Jim, et al. “Remarks on Suzuki’s Knot Epimorphism Number.” Journal of Knot Theory and Its Ramifications, vol. 28, no. 09, Aug. 2019. doi:10.1142/S0218216519500603.
Digital Commons @ LMU & LLS Citation
Shanahan, Patrick, "Remarks on Suzuki's epimorphism number" (2019). Mathematics, Statistics and Data Science Faculty Works. 163.
https://digitalcommons.lmu.edu/math_fac/163
