Deformations of dihedral representations
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- by Michael Heusener and Eric Klassen PDF
- Proc. Amer. Math. Soc. 125 (1997), 3039-3047 Request permission
Abstract:
G. Burde proved (1990) that the $\mathrm {SU}$ 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 $k \subset S^3$ we denote by $\hat {C}_2$ its twofold branched covering space. Assume that there is a prime number $p$ such that $H_1(\hat {C}_2,\mathbb {Z}_p)\cong \mathbb {Z}_p$. Then there exist representations of the knot group onto the binary dihedral group $D_p \subset \mathrm {SU}$ and these representations are smooth points on a one-dimensional curve of representations into $\mathrm {SU}$.References
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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
- 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
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 3039-3047
- MSC (1991): Primary 57M25, 57M05
- DOI: https://doi.org/10.1090/S0002-9939-97-04195-6
- MathSciNet review: 1443155