Finiteness of the number of arithmetic groups generated by reflections in Lobachevsky spaces
Finiteness of the number of arithmetic groups generated by reflections in Lobachevsky spaces
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洛巴切夫斯基空间中反射生成的算术群数量的有限性
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发表时间：
2006
期刊：
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通讯作者：
V. Nikulin
中科院分区：
文献类型：
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作者：
V. Nikulin
在作者（1980，1981）和Vinberg（1981）的结果之后，在Lobachevsky空间中由反射生成的极大算术群的个数的有限性只在维数上是未知的。最近（2005年）Long，Maclachlan和Reid在2维中证明了它，Agol在3维中证明了它。在这里，我们使用2维和3维的结果来证明所有剩余维的有限性。作者（1980，1981）的方法用一个非常简短和非常简单的论证就足以说明这一点。
After results of the author (1980, 1981) and Vinberg (1981), the finiteness of the number of maximal arithmetic groups generated by reflections in Lobachevsky spaces remained unknown in dimensions only. It was proved recently (2005) in dimension 2 by Long, Maclachlan and Reid and in dimension 3 by Agol. Here we use the results in dimensions 2 and 3 to prove the finiteness in all remaining dimensions . The methods of the author (1980, 1981) are more than sufficient for this using a very short and very simple argument.