Finiteness of arithmetic Kleinian reflection groups
نویسنده
چکیده
We prove that there are only finitely many arithmetic Kleinian maximal reflection groups. Mathematics Subject Classification (2000). Primary 30F40; Secondary 57M.
منابع مشابه
On fields of definition of arithmetic Kleinian reflection groups
We show that degrees of the real fields of definition of arithmetic Kleinian reflection groups are bounded by 35.
متن کاملMikhail v. Belolipetsky List of Publications
[1] Estimates for the number of automorphisms of a Riemann surface, Sib. Math. J. 38 (1997), no. 5, 860–867. [2] On Wiman bound for arithmetic Riemann surfaces, with Grzegorz Gromadzki, Glasgow Math. J. 45 (2003), 173–177. [3] Cells and representations of right-angled Coxeter groups, Selecta Math., N. S. 10 (2004), 325–339. [4] On volumes of arithmetic quotients of SO(1,n), Ann. Scuola Norm. Su...
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We prove that there are only finitely many conjugacy classes of arithmetic maximal hyperbolic reflection groups.
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Using authors’s methods of 1980, 1981, some explicit finite sets of number fields containing ground fields of arithmetic hyperbolic reflection groups are defined, and good bounds of their degrees (over Q) are obtained. For example, degree of the ground field of any arithmetic hyperbolic reflection group in dimension at least 6 is bounded by 56. These results could be important for further class...
متن کاملOn Finiteness of Kleinian Groups in General Dimension
In this paper we provide a criteria for geometric finiteness of Kleinian groups in general dimension. We formulate the concept of conformal finiteness for Kleinian groups in space of dimension higher than two, which generalizes the notion of analytic finiteness in dimension two. Then we extend the argument in the paper of Bishop and Jones to show that conformal finiteness implies geometric fini...
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تاریخ انتشار 2008