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2017 Epimorphisms between $2$–bridge knot groups and their crossing numbers
Masaaki Suzuki
Algebr. Geom. Topol. 17(4): 2413-2428 (2017). DOI: 10.2140/agt.2017.17.2413

Abstract

Suppose that there exists an epimorphism from the knot group of a 2–bridge knot K onto that of another knot K. We study the relationship between their crossing numbers c(K) and c(K). More specifically, it is shown that c(K) is greater than or equal to 3c(K), and we estimate how many knot groups a 2–bridge knot group maps onto. Moreover, we formulate the generating function which determines the number of 2–bridge knot groups admitting epimorphisms onto the knot group of a given 2–bridge knot.

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Masaaki Suzuki. "Epimorphisms between $2$–bridge knot groups and their crossing numbers." Algebr. Geom. Topol. 17 (4) 2413 - 2428, 2017. https://doi.org/10.2140/agt.2017.17.2413

Information

Received: 15 June 2016; Revised: 1 October 2016; Accepted: 3 December 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1372.57021
MathSciNet: MR3686401
Digital Object Identifier: 10.2140/agt.2017.17.2413

Subjects:
Primary: 57M25
Secondary: 57M27

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.17 • No. 4 • 2017
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