N ov 2 00 8 COUNTING ARITHMETIC LATTICES AND SURFACES
نویسنده
چکیده
We give estimates on the number ALH(x) of arithmetic lattices Γ of covolume at most x in a simple Lie group H . In particular, we obtain a first concrete estimate on the number of arithmetic 3-manifolds of volume at most x. Our main result is for the classical case H = PSL(2,R) where we show that lim x→∞ log ALH(x) x log x = 1 2π . The proofs use several different techniques: geometric (bounding the number of generators of Γ as a function of its covolume), number theoretic (bounding the number of maximal such Γ) and sharp estimates on the character values of the symmetric groups (to bound the subgroup growth of Γ).
منابع مشابه
N ov 2 00 5 Limit groups , positive - genus towers and measure equivalence
An ω-residually free tower is positive-genus if all surfaces used in its construction are of positive genus. We prove that every limit group is virtually a subgroup of a positive-genus ω-residually free tower. By combining this with results of Gaboriau, we prove that elementarily free groups are measure equivalent to free groups. Measure equivalence was introduced by M. Gromov in [8] as a measu...
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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