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International Conference of Steklov Institute Members, working outside Russia
June 6, 2009 12:30, Moscow
 


On classification of arithmetic groups generated by reflections in Lobachevsky spaces

V. V. Nikulin
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V. V. Nikulin


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Abstract: In 1980, 1981, I showed finiteness of the number of maximal arithmetic hyperbolic reflection groups in each fixed dimension $n\ge 10$. In 1981, Vinberg showed that $n\le 29$.
Only in 2005, Long–Maclachlan–Reid proved finiteness in dimension $n=2$, and Agol — in dimension $n=3$. In 2006, I showed finiteness in remaining dimensions $4\le n\le 9$. In 2007, I also proved effective finiteness in all dimensions.
In my talk, I outline these results.

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