English

Geometric finiteness in negatively pinched Hadamard manifolds

Group Theory 2018-12-24 v3 Differential Geometry Geometric Topology

Abstract

In this paper, we generalize Bonahon's characterization of geometrically infinite torsion-free discrete subgroups of PSL(2, C\mathbb{C}) to geometrically infinite discrete subgroups Γ\Gamma of isometries of negatively pinched Hadamard manifolds XX. We then generalize a theorem of Bishop to prove that every discrete geometrically infinite isometry subgroup Γ\Gamma has a set of nonconical limit points with the cardinality of the continuum.

Keywords

Cite

@article{arxiv.1801.08239,
  title  = {Geometric finiteness in negatively pinched Hadamard manifolds},
  author = {Michael Kapovich and Beibei Liu},
  journal= {arXiv preprint arXiv:1801.08239},
  year   = {2018}
}

Comments

We improved our results to any discrete geometrically infinite isometry subgroup of a negatively pinched Hadamard manifold, and we sharpened our main results to deal with limit sets of ends of the convex core