Geometry & Topology 14 (2010) 1383–1477

DOI: 10.2140/gt.2010.14.1383

Abstract

We describe a family of 4–dimensional hyperbolic orbifolds, constructed by deforming an infinite volume orbifold obtained from the ideal, hyperbolic 24–cell by removing two walls. This family provides an infinite number of infinitesimally rigid, infinite covolume, geometrically finite discrete subgroups of Isom(H⁴). It also leads to finite covolume Coxeter groups which are the homomorphic image of the group of reflections in the hyperbolic 24–cell. The examples are constructed very explicitly, both from an algebraic and a geometric point of view. The method used can be viewed as a 4–dimensional, but infinite volume, analog of 3–dimensional hyperbolic Dehn filling.

Keywords

hyperbolic manifold, discrete group

Mathematical Subject Classification

Primary: 22E40

Secondary: 20F55, 20H10, 51M99

References

Publication

Received: 25 August 2008
Revised: 18 May 2010
Accepted: 22 March 2010
Published: 7 June 2010
Proposed: Benson Farb
Seconded: Walter Neumann, Jean-Pierre Otal

Authors