Deformations of dihedral representations

Authors:
Michael Heusener and Eric Klassen

Journal:
Proc. Amer. Math. Soc. **125** (1997), 3039-3047

MSC (1991):
Primary 57M25, 57M05

MathSciNet review:
1443155

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Abstract | References | Similar Articles | Additional Information

Abstract: G. Burde proved (1990) that the representation space of two-bridge knot groups is one-dimensional. The same holds for all torus knot groups. The aim of this note is to prove the following:

Given a knot we denote by its twofold branched covering space. Assume that there is a prime number such that . Then there exist representations of the knot group onto the binary dihedral group and these representations are smooth points on a one-dimensional curve of representations into .

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Additional Information

**Michael Heusener**

Affiliation:
Uni–GH–Siegen Fachbereich Mathematik Hölderlinstraße 3 57068 Siegen Germany

Email:
heusener@hrz.uni-siegen.d400.de

**Eric Klassen**

Affiliation:
Department of Mathematics Florida State University Tallahassee Florida 32306

Email:
klassen@math.fsu.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-97-04195-6

Keywords:
Knot groups,
group representations,
$\SU$

Received by editor(s):
September 7, 1993

Additional Notes:
The second author was supported in part by a National Science Foundation Postdoctoral Research Fellowship.

Communicated by:
Ronald Stern

Article copyright:
© Copyright 1997
American Mathematical Society