Article contents
Non-injective representations of a closed surface group into PSL(2, )
Published online by Cambridge University Press: 10 April 2007
Abstract
Let e denote the Euler class on the space of representations of the fundamental group Γg of the closed surface Σg of genus g. Goldman showed that the connected components of are precisely the inverse images e−1(k), for 2−2g≤ k≤ 2g−2, and that the components of Euler class 2−2g and 2g−2 consist of the injective representations whose image is a discrete subgroup of . We prove that non-faithful representations are dense in all the other components. We show that the image of a discrete representation essentially determines its Euler class. Moreover, we show that for every genus and possible corresponding Euler class, there exist discrete representations.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 2 , March 2007 , pp. 289 - 304
- Copyright
- Copyright © Cambridge Philosophical Society 2007
References
REFERENCES
- 4
- Cited by