Primeness of twisted knots
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- by Kimihiko Motegi PDF
- Proc. Amer. Math. Soc. 119 (1993), 979-983 Request permission
Abstract:
Let $V$ be a standardly embedded solid torus in ${S^3}$ with a meridian-preferred longitude pair $(\mu ,\lambda )$ and $K$ a knot contained in $V$. We assume that $K$ is unknotted in ${S^3}$. Let ${f_n}$ be an orientation-preserving homeomorphism of $V$ which sends $\lambda$ to $\lambda + n\mu$. Then we get a twisted knot ${K_n} = {f_n}(K)$ in ${S^3}$. Primeness of twisted knots is discussed and we prove: A twisted knot ${K_n}$ is prime if $|n| > 5$. Moreover, ${\{ {K_n}\} _{n \in Z}}$ contains at most five composite knots.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 119 (1993), 979-983
- MSC: Primary 57M25
- DOI: https://doi.org/10.1090/S0002-9939-1993-1181171-5
- MathSciNet review: 1181171