Arithmetic cusp shapes are dense
Abstract
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 crosssection 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606508
 Bibcode:
 2006math......6508M
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Group Theory
 EPrint:
 Revised after referee report. 11 pages. To appear in Geom. Dedicata