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Izvestiya: Mathematics, 2007, Volume 71, Issue 1, Pages 53–56
DOI: https://doi.org/10.1070/IM2007v071n01ABEH002349 (Mi im1148) 		 
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
English version PDF (163 kB) Citations (27)
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DOI: https://doi.org/10.1070/IM2007v071n01ABEH002349
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
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2007, Volume 71, Issue 1, Pages 55–60
DOI: https://doi.org/10.4213/im1148
Bibliographic databases:
Document Type: Article
UDC: 512.817.72+512.817.6
MSC: 20F55, 51F15, 22E40
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 27 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:207
    English version PDF:5
    References:57
    First page:7
     
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