Algebraic & Geometric Topology 4 (2004) 721–755

DOI: 10.2140/agt.2004.4.721

arXiv: math.GT/0409278

Abstract

For X = R, C, or H, it is well known that cusp cross-sections of finite volume X–hyperbolic (n+1)–orbifolds are flat n–orbifolds or almost flat orbifolds modelled on the (2n+1)–dimensional Heisenberg group N_2n+1 or the (4n+3)–dimensional quaternionic Heisenberg group N_4n+3(H). We give a necessary and sufficient condition for such manifolds to be diffeomorphic to a cusp cross-section of an arithmetic X–hyperbolic (n+1)–orbifold.

A principal tool in the proof of this classification theorem is a subgroup separability result which may be of independent interest.

Keywords

Borel subgroup, cusp cross-section, hyperbolic space, nil manifold, subgroup separability.

Mathematical Subject Classification

Primary: 57M50

Secondary: 20G20

References

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Publication

Received: 2 April 2004
Revised: 24
Accepted: 3 September 2004
Published: 11 September 2004

Authors