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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On representations of the group of Listing's knot by subgroups of $ {\rm SL}(2,\,C)$


Author: Alice Whittemore
Journal: Proc. Amer. Math. Soc. 40 (1973), 378-382
MSC: Primary 20C05; Secondary 20H10, 55A25
MathSciNet review: 0316585
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Abstract: The subgroups $ G$ of $ SL(2,C)$ which represent the group of Listing's knot are characterized by the traces of $ A,B$ and $ AB$, where $ A$ and $ B$ are matrices which generate $ G$. From this it follows that there exist finitely generated nondiscrete subgroups of $ SL(2,R)$ which are not isomorphic to any Fuchsian group.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0316585-3
PII: S 0002-9939(1973)0316585-3
Keywords: Knot group, Listing knot, braid automorphism of free group, character manifold, elliptic and parabolic transformations, discrete subgroups of $ SL(2,C)$
Article copyright: © Copyright 1973 American Mathematical Society