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2004 Peripheral separability and cusps of arithmetic hyperbolic orbifolds
D B McReynolds
Algebr. Geom. Topol. 4(2): 721-755 (2004). DOI: 10.2140/agt.2004.4.721

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.

Citation

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D B McReynolds. "Peripheral separability and cusps of arithmetic hyperbolic orbifolds." Algebr. Geom. Topol. 4 (2) 721 - 755, 2004. https://doi.org/10.2140/agt.2004.4.721

Information

Received: 2 April 2004; Accepted: 3 September 2004; Published: 2004
First available in Project Euclid: 21 December 2017

zbMATH: 1058.57012
MathSciNet: MR2100678
Digital Object Identifier: 10.2140/agt.2004.4.721

Subjects:
Primary: 57M50
Secondary: 20G20

Rights: Copyright © 2004 Mathematical Sciences Publishers

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