Peripheral separability and cusps of arithmetic hyperbolic orbifolds

Details Peripheral separability and cusps of arithmetic hyperbolic orbifolds Peripheral separability and cusps of arithmetic hyperbolic orbifolds

2004-09-16

arxiv.org/abs/math/0409278v1

Algebr. Geom. Topol. 4 (2004) 721-755

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-32.abs.html

Scientific paper

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 N_{2n+1} or the (4n+3)-dimensional quaternionic Heisenberg group N_{4n+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.

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