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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Peripherally specified homomorphs of knot groups


Authors: Dennis Johnson and Charles Livingston
Journal: Trans. Amer. Math. Soc. 311 (1989), 135-146
MSC: Primary 57M25
MathSciNet review: 942427
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0942427-5
PII: S 0002-9947(1989)0942427-5
Article copyright: © Copyright 1989 American Mathematical Society