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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 PSL2 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