Peripheral separability and cusps of arithmetic hyperbolic orbifolds.
Peripheral separability and cusps of arithmetic hyperbolic orbifolds.
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算术双曲轨道折叠的周边可分离性和尖点。
DOI：
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发表时间：
2004
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通讯作者：
David Ben McReynolds
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作者：
David Ben McReynolds
对于 X = R、C 或 H，众所周知，有限体积 X 双曲 (n + 1) 轨道的尖点横截面是平坦的 n 轨道或几乎平坦的轨道，以 (2n +1) 维海森堡群 n 2 n + 1 或 (4n + 3) 维四元数海森堡群 n 4 n + 3 为模型 (H) 我们给出了这样的充分必要条件流形与算术 X 双曲 (n + 1) 轨道折叠的尖点横截面微分同胚。证明该分类定理的主要工具是可能具有独立意义的子群可分离性结果。
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 2 n + 1 orthe (4n + 3)-dimensional quaternionic Heisenberg group n 4 n + 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.