Research ArticleNo Access

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

Masaaki Suzuki

Department of Frontier Media Science, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo 164-8525, Japan

https://doi.org/10.1142/S0218216521500735Cited by:0 (Source: Crossref)

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:

AMSC: 57K10, 57M05

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