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)



Representing knot groups into $ {\rm SL}(2,{\bf C})$

Authors: D. Cooper and D. D. Long
Journal: Proc. Amer. Math. Soc. 116 (1992), 547-549
MSC: Primary 57M25
MathSciNet review: 1100647
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that if a knot in $ {S^3}$ has nontrivial Alexander polynomial then the fundamental group of its complement has a representation into $ \operatorname{SL}(2,{\mathbf{C}})$ whose image contains a free group of rank two.

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

  • [BZ] G. Burde and H. Zeischang, Knots, de Gruyter Stud. Math., vol. 5, de Gruyter, Berlin, 1985.
  • [CS] M. Culler and P. B. Shalen, Varieties of group representations and splittings of $ 3$-manifolds, Ann. of Math. (2) 117 (1983), 109-146. MR 683804 (84k:57005)
  • [CC] D. Cooper, M. Culler, H. Gillet, D. D. Long, and P. B. Shalen, Plane curves associated to character varieties of $ 3$-manifolds, preprint.
  • [T] W. P. Thurston, The geometry and topology of $ 3$-manifolds, preprint.
  • [S] T. Soma, On preimage knots in $ {S^3}$, Proc Amer. Math. Soc. 100 (1987), 589-592. MR 891169 (88e:57011)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57M25

Retrieve articles in all journals with MSC: 57M25

Additional Information

Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society