Epimorphisms between $2$-bridge knot groups and their crossing numbers

Masaaki Suzuki

doi:10.2140/agt.2017.17.2413

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arXiv · 1606.04677

Epimorphisms between $2$-bridge knot groups and their crossing numbers

Masaaki Suzuki

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Abstract

Suppose that there exists an epimorphism from the knot group of a $2$-bridge knot $K$ onto that of another knot $K'$. In this paper, we study the relationship between their crossing numbers $c(K)$ and $c(K')$. Especially it is shown that $c(K)$ is greater than or equal to $3 c(K')$ 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. 2016-06-15. Epimorphisms between $2$-bridge knot groups and their crossing numbers. https://doi.org/10.2140/agt.2017.17.2413

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