Keywords

constant curvature, dimension 3, Gromov hyperbolic, Riemann mapping theorem, Sullivan-Tukia theorem

Abstract

We characterize those discrete groups Gwhich can act properly discontinuously, isometrically, and cocompactly on hyperbolic 3-space H^3 in terms of the combinatorics of the action of G on its space at infinity. The major ingredients in the proof are the properties of groups that are negatively curved (in the large) (that is, Gromov hyperbolic), the combinatorial Riemann mapping theorem, and the Sullivan-Tukia theorem on groups which act uniformly quasiconformally on the 2-sphere.

Original Publication Citation

Michel, M. L., A. C. Keller, C. Paget, M. Fujio, F. Trottein, P. B. Savage, C.-H. Wong, E. Schneider, M. Dy, and M. C. Leite-De-Moraes (27, April). Identification of an il-17-producing nk1.1neg inkt cell population involved in airway neutrophilia. J. Ex