Counting Hyperbolic Manifolds with Bounded Diameter
نویسنده
چکیده
Let ρn(V ) be the number of complete hyperbolic manifolds of dimension n with volume less than V . Burger, Gelander, Lubotzky, and Moses[2] showed that when n ≥ 4 there exist a, b > 0 depending on the dimension such that aV logV ≤ log ρn(V ) ≤ bV logV, for V ≫ 0. In this note, we use their methods to bound the number of hyperbolic manifolds with diameter less than d and show that the number grows double-exponentially. Additionally, this bound holds in dimension 3.
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تاریخ انتشار 2006