Peripherally specified homomorphs of knot groups

Johnson, Dennis; Livingston, Charles

doi:10.1090/S0002-9947-1989-0942427-5

Peripherally specified homomorphs of knot groups
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by Dennis Johnson and Charles Livingston

Trans. Amer. Math. Soc. 311 (1989), 135-146

DOI: https://doi.org/10.1090/S0002-9947-1989-0942427-5

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Abstract:

Let $G$ be a group and let $\mu$ and $\lambda$ be elements of $G$. Necessary and sufficient conditions are presented for the solution of the following problem: Is there a knot $K$ in ${S^3}$ and a representation $\rho :{\pi _1}({S^3} - K) \to G$ such that $\rho (m) = \mu$ and $\rho (l) = \lambda$, where $m$ and $l$ are the meridian and longitude of $K$?

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Peripherally specified homomorphs of knot groups

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