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Finiteness of the number of arithmetic groups generated by reflections in Lobachevsky spaces

Viacheslav V. Nikulin
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Abstract

After results by the author (1980, 1981), and by Vinberg (1981), finiteness of the number of maximal arithmetic reflection groups in Lobachevsky spaces was not known in dimensions $2\le n\le 9$ only. Recently (2005), the finiteness was proved in dimension 2 by Long, Maclachlan and Reid, and in dimension 3 by Agol. Here we use these results in dimensions 2 and 3 to prove finiteness in all remaining dimensions $4\le n\le 9$. Methods of the author (1980, 1981) are strong enough to complete this in few lines by simple considerations.

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Viacheslav V. Nikulin. 2006-09-27. Finiteness of the number of arithmetic groups generated by reflections in Lobachevsky spaces. https://doi.org/10.1070/im2007v071n01abeh002349

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