Remarks on Suzuki’s knot epimorphism number
Remarks on Suzuki’s knot epimorphism number
复制标题
铃木结外态数的评述
DOI：
10.1142/s0218216519500603
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发表时间：
2018
影响因子：
0.5
通讯作者：
Patrick D. Shanahan
中科院分区：
文献类型：
--
作者：
J. Hoste;Joshua Ocana Mercado;Patrick D. Shanahan
如果存在从[公式：见文]的结群到[公式：见文]的结群的外胚，则素结上的偏序可以通过声明[公式：见文]来定义。假设[公式：见文]是一个严格大于[公式：见文]不同的非平凡结的双桥结。本文用[公式：见文]确定了[公式：见文]交叉数的下界。利用这一界，我们回答了Suzuki关于2桥异态数的问题[公式：见文]，即严格小于具有交叉数的2桥结的非平凡结的最大数目。我们建立了我们的结果使用的技术与解析的连分数扩展的定义分数的2桥结。
A partial order on prime knots can be defined by declaring [Formula: see text], if there exists an epimorphism from the knot group of [Formula: see text] onto the knot group of [Formula: see text]. Suppose that [Formula: see text] is a 2-bridge knot that is strictly greater than [Formula: see text] distinct, nontrivial knots. In this paper, we determine a lower bound on the crossing number of [Formula: see text] in terms of [Formula: see text]. Using this bound, we answer a question of Suzuki regarding the 2-bridge epimorphism number [Formula: see text] which is the maximum number of nontrivial knots which are strictly smaller than some 2-bridge knot with crossing number [Formula: see text]. We establish our results using techniques associated with parsings of a continued fraction expansion of the defining fraction of a 2-bridge knot.