Work

Generating function on epimorphisms between $2$-bridge knot groups

Year: 2020

Type: preprint

Abstract: We have the generating function which determines the number of $2$-bridge knot groups admitting epimorphisms onto the knot group of a given $2$-bridge knot, in terms of crossing number. In this paper, we will refine this formula by taking account into genus as well as crossing number. Next, we determine the number of epimorphisms between fibered $2$-bridge knot groups. Moreover, we discuss degree one maps and $2$-bridge knots uknotting number one.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2010.06832

Author: Suzuki, Masaaki

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W3092990606

Cites: 17

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Related to: 10