Generating functions on epimorphisms between 2 -bridge knot groups

Masaaki Suzuki

doi:10.1142/S0218216521500735

Generating functions on epimorphisms between 2 -bridge knot groups

Masaaki Suzuki

Department of Frontier Media Science

Research output: Contribution to journal › Article › peer-review

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 into account 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 with unknotting number one.

Original language	English
Article number	2150073
Journal	Journal of Knot Theory and its Ramifications
Volume	30
Issue number	9
DOIs	https://doi.org/10.1142/S0218216521500735
Publication status	Published - 1 Aug 2021

Keywords

2 -bridge knots
Epimorphisms
Generating functions
Knot groups

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10.1142/S0218216521500735

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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 into account 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 with unknotting number one. ",

keywords = "2 -bridge knots, Epimorphisms, Generating functions, Knot groups",

author = "Masaaki Suzuki",

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N2 - 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 into account 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 with unknotting number one.

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KW - Epimorphisms

KW - Generating functions

KW - Knot groups

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ER -

Generating functions on epimorphisms between 2 -bridge knot groups

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