## Duke Mathematical Journal

### Surface groups are frequently faithful

#### Abstract

We show that the set of faithful representations of a closed orientable hyperbolic surface group is dense in both irreducible components of the $\mathrm{PSL}_2(\mathbb{K})$ representation variety, where $\mathbb{K}=\mathbb{C}$ or $\mathbb{R}$, answering a question of W. M. Goldman. We also prove the existence of faithful representations into $\mathrm{PU}(2,1)$ with certain nonintegral Toledo invariants.

#### Article information

Source
Duke Math. J., Volume 131, Number 2 (2006), 351-362.

Dates
First available in Project Euclid: 12 January 2006

https://projecteuclid.org/euclid.dmj/1137077887

Digital Object Identifier
doi:10.1215/S0012-7094-06-13125-3

Mathematical Reviews number (MathSciNet)
MR2219244

Zentralblatt MATH identifier
1109.57002

#### Citation

Deblois, Jason; Kent, Richard P. Surface groups are frequently faithful. Duke Math. J. 131 (2006), no. 2, 351--362. doi:10.1215/S0012-7094-06-13125-3. https://projecteuclid.org/euclid.dmj/1137077887

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