Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 4, Number 2 (2004), 721-755.
Peripheral separability and cusps of arithmetic hyperbolic orbifolds
For , , or , it is well known that cusp cross-sections of finite volume –hyperbolic –orbifolds are flat –orbifolds or almost flat orbifolds modelled on the –dimensional Heisenberg group or the –dimensional quaternionic Heisenberg group . We give a necessary and sufficient condition for such manifolds to be diffeomorphic to a cusp cross-section of an arithmetic –hyperbolic –orbifold.
A principal tool in the proof of this classification theorem is a subgroup separability result which may be of independent interest.
Algebr. Geom. Topol., Volume 4, Number 2 (2004), 721-755.
Received: 2 April 2004
Accepted: 3 September 2004
First available in Project Euclid: 21 December 2017
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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