Volume 4, issue 2 (2004)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Peripheral separability and cusps of arithmetic hyperbolic orbifolds

D B McReynolds

Algebraic & Geometric Topology 4 (2004) 721–755

arXiv: math.GT/0409278

Abstract

For X = , , or , 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 N2n+1 or the (4n + 3)–dimensional quaternionic Heisenberg group N4n+3(). 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 2000
Primary: 57M50
Secondary: 20G20
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Publication
Received: 2 April 2004
Accepted: 3 September 2004
Published: 11 September 2004
Authors
D B McReynolds
University of Texas
Austin TX 78712
USA