Arithmeticity, Discreteness and Volume
微分几何
2016-09-06 v1
摘要
We give an arithmetic criterion which is sufficient to imply the discreteness of various two-generator subgroups of . We then examine certain two-generator groups which arise as extremals in various geometric problems in the theory of Kleinian groups, in particular those encountered in efforts to determine the smallest co-volume, the Margulis constant and the minimal distance between elliptic axes. We establish the discreteness and arithmeticity of a number of these extremal groups, the associated minimal volume arithmetic group in the commensurability class and we study whether or not the axis of a generator is simple.
引用
@article{arxiv.math/9504208,
title = {Arithmeticity, Discreteness and Volume},
author = {F. W. Gehring and C. Maclachlan and G. J. Martin and A. W. Reid},
journal= {arXiv preprint arXiv:math/9504208},
year = {2016}
}