Algebraic and geometric convergence of discrete representations into PSL2ℂ

Biringer, Ian; Souto, Juan

doi:10.2140/gt.2010.14.2431

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Algebraic and geometric convergence of discrete representations into $\mathrm{PSL}_2\mathbb{C}$

Ian Biringer and Juan Souto

Geometry & Topology 14 (2010) 2431–2477

DOI: 10.2140/gt.2010.14.2431

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

References

Publication

Received: 24 April 2009

Accepted: 7 September 2010

Published: 4 December 2010

Proposed: Jean-Pierre Otal

Seconded: Danny Calegari, David Gabai

Authors

Ian Biringer
Department of Mathematics Yale University New Haven CT 06511 USA
http://www.math.yale.edu/~ib93
Juan Souto
Department of Mathematics University of Michigan Ann Arbor MI 48109 USA

Volume 14, issue 4 (2010)