Algebraic and geometric convergence of discrete representations into PSL2ℂ

Biringer, Ian¹ ; Souto, Juan²

¹ Department of Mathematics, Yale University, New Haven CT 06511, USA
² Department of Mathematics, University of Michigan, Ann Arbor MI 48109, USA

Geometry & topology, Tome 14 (2010) no. 4, pp. 2431-2477.

Résumé

Anderson and Canary have shown that if the algebraic limit of a sequence of discrete, faithful representations of a finitely generated group into ${PSL}_2ℂ$ 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.

Détail

DOI : 10.2140/gt.2010.14.2431

Keywords: hyperbolic manifold, algebraic convergence, geometric convergence

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