Abstract

We study several explicit finite index subgroups in the known complex hyperbolic lattice triangle groups, and show some of them are neat, some of them have positive first Betti number, some of them have a homomorphisms onto a non-Abelian free group. For some lattice triangle groups, we determine the minimal index of a neat subgroup. Finally, we answer a question raised by Stover and describe an infinite tower of neat ball quotients all with a single cusp.

中文翻译：

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关于复双曲格子三角形群的子群有限指数

摘要

我们研究了已知复双曲格子三角形群中的几个显式有限指数子群，发现其中有的是整群，有的具有正的第一贝蒂数，有的在非阿贝尔自由群上同态。对于一些格子三角形群，我们确定了一个整洁子群的最小索引。最后，我们回答了 Stover 提出的一个问题，并描述了一个无限的整齐球商塔，所有的塔都有一个尖点。