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.
"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