Remarks on Suzuki's Knot Epimorphism Number

Autor:	Hoste, Jim, Mercado, Joshua Ocana, Shanahan, Patrick D.
Rok vydání:	2018
Předmět:	Mathematics - Geometric Topology Mathematics - Algebraic Topology 57M25
Druh dokumentu:	Working Paper
Popis:	A partial order on prime knots can be defined by declaring $J\ge K$ if there exists an epimorphism from the knot group of $J$ onto the knot group of $K$. Suppose that $J$ is a 2-bridge knot that is strictly greater than $m$ distinct, nontrivial knots. In this paper we determine a lower bound on the crossing number of $J$ in terms of $m$. Using this bound we answer a question of Suzuki regarding the 2-bridge epimorphism number $\mbox{EK}(n)$ which is the maximum number of nontrivial knots which are strictly smaller than some 2-bridge knot with crossing number $n$. We establish our results using techniques associated to parsings of a continued fraction expansion of the defining fraction of a 2-bridge knot. Comment: 14 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1810.05146 Zobrazit plný text záznamu View this record from Arxiv