Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] E. Artin, Theorie der Zöpfe, Abh. Math. Sem. Univ. Hamburg 4 (1926), 47-72.
  • [2] R. Fricke and F. Klein, Vorlesungen über die Theorie der automorphen Functionen, Vol. 1, Teubner, Leipzig, 1897, pp. 338, 366.
  • [3] Robert D. Horowitz, Characters of free groups represented in the two-dimensional special linear group, Comm. Pure Appl. Math. 25 (1972), 635–649. MR 0314993
  • [4] A. W. Knapp, Doubly generated Fuchsian groups, Michigan Math. J. 15 (1969), 289–304. MR 0248231
  • [5] Wilhelm Magnus, Untersuchungen über einige unendliche diskontinuierliche Gruppen, Math. Ann. 105 (1931), no. 1, 52–74 (German). MR 1512704, 10.1007/BF01455808
  • [6] Gerhard Rosenberger, Automorphismen und Erzeugende für Gruppen mit einer definierenden Relation, Math. Z. 129 (1972), 259–267 (German). MR 0315003
  • [7] H. Zieschang, Unpublished.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20C05, 20H10, 55A25

Retrieve articles in all journals with MSC: 20C05, 20H10, 55A25

Additional Information

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