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On the number of ends of rank one locally symmetric spaces

Stover, M
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Journal Article
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2013-05-13
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math.GT
 math.GT
 math.DG
 math.NT
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http://hdl.handle.net/20.500.12613/5962
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1112.4495v2.pdf
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10.2140/gt.2013.17.905
Abstract
Let Y be a noncompact rank one locally symmetric space of finite volume. Then Y has a finite number e(Y) > 0 of topological ends. In this paper, we show that for any n ∈ N, the Y with e(Y) ≥ n that are arithmetic fall into finitely many commensurability classes. In particular, there is a constant cn such that n-cusped arithmetic orbifolds do not exist in dimension greater than cn. We make this explicit for one-cusped arithmetic hyperbolic n-orbifolds and prove that none exist for n ≥ 30.
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Mathematical Sciences Publishers
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Geometry and Topology
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