Convergence and divergence of Kleinian surface groups
arXiv:1407.4439 · doi:10.1112/jtopol/jtv014
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.
References in corpus (5)
- Geometry of the Complex of Curves I: Hyperbolicity
- Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle
- Asymptotic geometry of the mapping class group and Teichmueller space
- Kleinian groups and the complex of curves
- Local topology in deformation spaces of hyperbolic 3-manifolds