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This article is cited in 27 scientific papers (total in 27 papers)
Finiteness of the number of arithmetic groups generated by reflections in Lobachevsky spaces
V. V. Nikulinab a Steklov Mathematical Institute, Russian Academy of Sciences
b University of Liverpool
Abstract:
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
$2\le n\le 9$ 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 $4\le n\le 9$. The methods
of the author (1980, 1981) are more than sufficient for this
using a very short and very simple argument.
Received: 14.09.2006
Citation:
V. V. Nikulin, “Finiteness of the number of arithmetic groups generated by reflections in Lobachevsky spaces”, Izv. RAN. Ser. Mat., 71:1 (2007), 55–60; Izv. Math., 71:1 (2007), 53–56
Linking options:
https://www.mathnet.ru/eng/im1148https://doi.org/10.1070/IM2007v071n01ABEH002349 https://www.mathnet.ru/eng/im/v71/i1/p55
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Abstract page: | 587 | Russian version PDF: | 207 | English version PDF: | 5 | References: | 57 | First page: | 7 |
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