JournalscmhVol. 88, No. 4pp. 813–857

Strong convergence of Kleinian groups: the cracked eggshell

  • James W. Anderson

    University of Southampton, UK
  • Cyril Lecuire

    Université Paul Sabatier, Toulouse, France
Strong convergence of Kleinian groups: the cracked eggshell cover
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Abstract

In this paper we give a complete description of the set SH(π1(M))\mathrm{SH}(\pi_1(M)) of discrete faithful representations of the fundamental group of a compact, orientable, hyperbolizable 3-manifold 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(π1(M))\mathrm{SH}(\pi_1(M)) that extend the usual Ahlfors–Bers coordinates. We use these coordinates to show the local connectivity of SH(π1(M))\mathrm{SH}(\pi_1(M)) and study the action of the modular group of MM on SH(π1(M))\mathrm{SH}(\pi_1(M)).

Cite this article

James W. Anderson, Cyril Lecuire, Strong convergence of Kleinian groups: the cracked eggshell. Comment. Math. Helv. 88 (2013), no. 4, pp. 813–857

DOI 10.4171/CMH/304