Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-25T09:09:29.986Z Has data issue: false hasContentIssue false
  • English
  • Français

Roots of unity and the character variety of a knot complement

Part of: Low-dimensional topology Topological manifolds

Published online by Cambridge University Press:  09 April 2009

D. Cooper  and
D. D. Long
D. Cooper
Affiliation:
Department of Mathematics, University of California, Santa Barbara, Ca. 93106, USA
D. D. Long
Affiliation:
Department of Mathematics, University of California, Santa Barbara, Ca. 93106, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Using elementary methods we give a new proof of a result concerning the special form of the character of the bounded peripheral element which arises at an end of a curve component of the character variety of a knot complement.

MSC classification

Secondary: 57M25: Knots and links in $S^3$ 57N10: Topology of general $3$-manifolds
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 55 , Issue 1 , August 1993 , pp. 90 - 99
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Bestvina, M., ‘Degenerations of the hyperbolic space’, Duke J. Math. 56 (1988), 142–161.CrossRefGoogle Scholar
[2]Cooper, D., ‘Degenerations of representations in SL(2,C)’, preprint.Google Scholar
[3]Culler, M., Cooper, D., Gillett, H., Long, D. D. and Shalen, P. B., ‘Plane curves associated to character varieties of knot complements’, preprint.Google Scholar
[4]Culler, M. and Morgan, J., ‘Group actions on R-trees’, Proc. London Math. Soc. 55 (1987), 571–604.CrossRefGoogle Scholar
[5]Culler, M. and Shalen, P. B., ‘Varieties of group representations and splittings of 3-manifolds’, Ann. of Math. 117 (1983), 109–145.CrossRefGoogle Scholar
[6]Hatcher, A. and Thurston, W. P., ‘Incompressible surfaces in two bridge knot complements’, Invent. Math. 79 (1985), 225–246.CrossRefGoogle Scholar