On the number of ends of rank one locally symmetric spaces

Details On the number of ends of rank one locally symmetric spaces On the number of ends of rank one locally symmetric spaces

2011-12-19

arxiv.org/abs/1112.4495v1

Mathematics

Geometric Topology

Scientific paper

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 natural number n, the Y with e(Y) \leq n that are arithmetic fall into finitely many commensurability classes. In particular, there is a constant c_n such that n-cusped arithmetic orbifolds do not exist in dimension greater than c_n. We make this explicit for one-cusped arithmetic hyperbolic n-orbifolds and prove that none exist for n \geq 30.

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