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Media type:
E-Article
Title:
Deformations of Dihedral Representations
Contributor:
Heusener, Michael;
Klassen, Eric
imprint:
American Mathematical Society, 1997
Published in:Proceedings of the American Mathematical Society
Language:
English
ISSN:
0002-9939;
1088-6826
Origination:
Footnote:
Description:
<p>G. Burde proved (1990) that the SU<sub>2</sub>(C) 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<tex-math>$k \subset S^3$</tex-math>we denote by<tex-math>$\hat C_2$</tex-math>its twofold branched covering space. Assume that there is a prime number p such that<tex-math>$H_1(\hat C_2, \mathbb{Z}_p) \cong \mathbb{Z}_p$</tex-math>. Then there exist representations of the knot group onto the binary dihedral group<tex-math>$D_p \subset \mathrm{SU}_2(\mathbb{C})$</tex-math>and these representations are smooth points on a one-dimensional curve of representations into SU<sub>2</sub>(C).</p>