Peripheral separability and cusps of arithmetic hyperbolic orbifolds

McReynolds, D B¹

¹University of Texas, Austin TX 78712, USA

Algebraic and Geometric Topology, Tome 4 (2004) no. 2, pp. 721-755

Résumé

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 N2n+1 or the (4n + 3)–dimensional quaternionic Heisenberg group N4n+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.

Détail

DOI : 10.2140/agt.2004.4.721

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

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