Sociology of Kleinian Groups

Part of the Modern Birkhäuser Classics book series (MBC)


Let G be a Lie group and Г a finitely generated group. A representation ρ : Г → G is said to be discrete if its image is a discrete subgroup of G. A representation is said to be faithful if it is a monomorphism. Definition 8.1. Suppose that ρj is a sequence of representations of Г to G. Then the sequence ρj is said to be algebraically convergent to a representation ρ iff for each g ϵ Г, we have
$$\mathop {\lim }\limits_{n \to \infty } \rho j(g) = \rho (g),$$
Where convergence is understood in the topology of the Lie group G. The topology of algebraic convergence is consistent with the usual topology of the representation variety R 0 (Г, G). This is the most intutively obvious concept of convergence of representations. As we shall see, there are some other definitions of convergence that differ from this one.


Riemann Surface Kleinian Group Fuchsian Group Rigidity Theorem Beltrami Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Boston 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California, DavisDavisU.S.A.

Personalised recommendations