Convergence and divergence of Kleinian surface groups

Jeffrey Brock; Kenneth Bromberg; Richard Canary; Cyril Lecuire

doi:10.1112/jtopol/jtv014

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arXiv · 1407.4439

Convergence and divergence of Kleinian surface groups

Jeffrey Brock·Kenneth Bromberg·Richard Canary·Cyril Lecuire

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Abstract

We characterize sequences of Kleinian surface groups with convergent subsequences in terms of the asymptotic behavior of the ending invariants of the associated hyperbolic 3-manifolds. Asymptotic behavior of end invariants in a convergent sequence predicts the parabolic locus of the algebraic limit as well as how the algebraic limit wraps within the geometric limit under the natural locally isometric covering map.

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Jeffrey Brock, Kenneth Bromberg, Richard Canary, Cyril Lecuire. 2014-07-16. Convergence and divergence of Kleinian surface groups. https://doi.org/10.1112/jtopol%2Fjtv014

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