## Algebraic & Geometric Topology

### Peripheral separability and cusps of arithmetic hyperbolic orbifolds

D B McReynolds

#### 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 $N2n+1$ 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 4, Number 2 (2004), 721-755.

Dates
Accepted: 3 September 2004
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.agt/1513882529

Digital Object Identifier
doi:10.2140/agt.2004.4.721

Mathematical Reviews number (MathSciNet)
MR2100678

Zentralblatt MATH identifier
1058.57012

#### Citation

McReynolds, D B. Peripheral separability and cusps of arithmetic hyperbolic orbifolds. Algebr. Geom. Topol. 4 (2004), no. 2, 721--755. doi:10.2140/agt.2004.4.721. https://projecteuclid.org/euclid.agt/1513882529

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