Finiteness of the number of arithmetic groups generated by reflections in Lobachevsky spaces
نویسنده
چکیده
After results by the author (1980, 1981) and Vinberg (1981), finiteness of the number of maximal arithmetic groups generated by reflections in Lobachevsky spaces was not known in dimensions 2 ≤ n ≤ 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 ≤ n ≤ 9. Methods of the author (1980, 1981) are more than sufficient to prove this by a very short and very simple consideration.
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