English

Strong convergence of Kleinian groups: the cracked eggshell

Geometric Topology 2013-10-28 v2 Differential Geometry

Abstract

In this paper we give a complete description of the set of discrete faithful representations SH(M) uniformizing a compact, orientable, hyperbolizable 3-manifold M with incompressible boundary, equipped with the strong topology, with the description given in term of the end invariants of the quotient manifolds. As part of this description, we introduce coordinates on SH(M) that extend the usual Ahlfors-Bers coordinates. We use these coordinates to show the local connectivity of SH(M) and study the action of the modular group of M on SH(M).

Keywords

Cite

@article{arxiv.1003.1843,
  title  = {Strong convergence of Kleinian groups: the cracked eggshell},
  author = {James W. Anderson and Cyril Lecuire},
  journal= {arXiv preprint arXiv:1003.1843},
  year   = {2013}
}

Comments

To appear in Commentarii Math. Helvetici, 37 pages, 2 figures, final version

R2 v1 2026-06-21T14:55:28.306Z