Arithmetic cusp shapes are dense

被引：2
|
作者：
McReynolds, D. B. [1 ]
机构：
[1] CALTECH, Dept Math, Pasadena, CA 91125 USA
来源：
GEOMETRIAE DEDICATA | 2007年 / 129卷 / 01期
关键词：
arithmetic orbifolds; cusp cross-section; flat manifolds; hyperbolic manifolds; selberg's lemma;
D O I：
10.1007/s10711-007-9192-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article we verify an orbifold version of a conjecture of Nimershiem from 1998. Namely, for every flat n-manifold M, we show that the set of similarity classes of flat metrics on M which occur as a cusp cross-section of a hyperbolic (n + 1)-orbifold is dense in the space of similarity classes of flat metrics on M. The set used for density is precisely the set of those classes which arise in arithmetic orbifolds.
引用
收藏
页码：47 / 55
页数：9
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