#### Volume 14, issue 4 (2010)

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 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
Algebraic and geometric convergence of discrete representations into $\mathrm{PSL}_2\mathbb{C}$

### Ian Biringer and Juan Souto

Geometry & Topology 14 (2010) 2431–2477
##### Abstract

Anderson and Canary have shown that if the algebraic limit of a sequence of discrete, faithful representations of a finitely generated group into ${PSL}_{2}ℂ$ does not contain parabolics, then it is also the sequence’s geometric limit. We construct examples that demonstrate the failure of this theorem for certain sequences of unfaithful representations, and offer a suitable replacement.

##### Keywords
hyperbolic manifold, algebraic convergence, geometric convergence