Counting arithmetic lattices and surfaces
Webarithmetic lattices of the simplest type appears as a combination of[28]and Agol[3]. In particular, it covers the case of all nonuniform arithmetic lattices (n 4) and all arithmetic lattices in O.n;1/for n even, since they are of the simplest type. For odd n ⁄3;7, there are also arithmetic lattices in O.n;1/of “quaternionic origin” Webthe methods of [10] (that build on those of [11]) she is able to construct examples of thin surface subgroups in any cocompact lattice contained in SL(3;R). Regarding Theorem 1.1, one can say rather more for certain lattices. In the notation established below, we construct explicit lattices in SL(3;R) that contain thin surface subgroups. (We ...
Counting arithmetic lattices and surfaces
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WebArithmetic Kleinian groups are arithmetic lattices in $\mathrm {PSL}_2(\mathbb {C})$. We present an algorithm that, given such a group $\Gamma$, returns a fundamental domain and a finite presentation for $\Gamma$ with a computable isomorphism. ... Alexander Lubotzky, and Aner Shalev, Counting arithmetic lattices and surfaces, Ann. of Math. … WebCounting arithmetic lattices and surfaces, with Tsachik Gelander, Alex Lubotzky and Aner Shalev, Ann. of Math. (2) 172 (2010), 2197–2221. [14] Systoles of hyperbolic manifolds, with Scott Thomson, Algebr. Geom. Topol. 11 (2011), 1455–1469. [15] Finiteness theorems for congruence reflection groups, Transform. Groups 16 (2011), 939–954. [16]
WebCounting arithmetic lattices and surfaces By MIKHAIL BELOLIPETSKY, TSACHIK GELANDER, ALEXANDER LUBOTZKY, and ANER SHALEV Abstract We give estimates on the number ALH .x/ of conjugacy classes of arithmetic lattices of covolume at most x in a simple Lie groupH . WebApr 30, 2024 · In [BGLM] and [GLNP] it was conjectured that if H is a simple Lie group of real rank at least 2, then the number of conjugacy classes of (arithmetic) lattices in H of …
WebCOUNTING ARITHMETIC LATTICES AND SURFACES 2199 other applications, for instance, it gives a linear bound on the first Betti number of orbifolds in terms of … WebDec 16, 2016 · We prove that cocompact arithmetic lattices in a simple Lie group are uniformly discrete if and only if the Salem numbers are uniformly bounded away from 1. We also prove an analogous… Expand PDF A VIEW ON INVARIANT RANDOM SUBGROUPS AND LATTICES T. Gelander Mathematics Proceedings of the International Congress of …
WebAug 1, 2014 · Belolipetsky M.: Counting maximal arithmetic subgroups. With an appendix by Jordan Ellenberg and Akshay Venkatesh. Duke Mathematical Journal 1(140), 1–33 …
WebCounting arithmetic lattices and surfaces Pages 2197-2221 from Volume 172 (2010), Issue 3 by Mikhail Belolipetsky, Tsachik Gelander, Alexander Lubotzky, Aner Shalev Abstract We give estimates on the number AL H ( x) of conjugacy classes of arithmetic … Abstract. In this note we show that the quotient field of a domain which is … Subgroup Growth - Counting arithmetic lattices and surfaces Annals of … 20E07 - Counting arithmetic lattices and surfaces Annals of Mathematics Minimal co-volume hyperbolic lattices, I: The spherical points of a Kleinian group. … Compact moduli of K3 surfaces. by Valery Alexeev, Philip Engel. Wall crossing for … Editorial, Electronic Licensing Agreement, and Production Matters: For the … Submissions should be sent electronically and in PDF format either to the Annals … 20C30 - Counting arithmetic lattices and surfaces Annals of Mathematics Fuchsian Groups - Counting arithmetic lattices and surfaces Annals of … Articles with article keyword: counting lattices. Counting arithmetic lattices and … gerris conformisWebMoreover, Serre conjectured ([S]) that for all lattices Γ in such H, Γ has the con-gruence subgroup property (CSP), i.e. Ker(\G(O) → G(Ob)) is finite in the notations above. Assuming the conjecture, the question of counting lattices in H boils down to counting arithmetic groups and their congruence subgroups. A related conjecture christmas events in huntersville ncWebCOUNTING ARITHMETIC LATTICES AND SURFACES MIKHAIL BELOLIPETSKY, TSACHIK GELANDER, ALEX LUBOTZKY, AND ANER SHALEV Abstract. We give … christmas events in hertfordshire 2022Websurfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in R 3 R3. In this chapter, they also discuss plane lattices. By considering unit lattices, and throwing in a small amount of gerris grooming colorado springsWebdenote the number of maximal uniform arithmetic lattices of covolume vin Isom+(Hn). The following theorem is due to Belolipetsky [Bel07] in dimension n 4 andBelolipetsky,Gelander,LubotzkyandShalev[BGLS10]indimensions ... Counting arithmetic lattices and surfaces. Ann. of Math. (2), 172(3):2197–2221, 2010. christmas events in hertfordshireWebNov 1, 2024 · A major impetus behind this paper was to improve upon for automorphic forms of minimal type on compact arithmetic surfaces. One consequence of Theorem A is that we can now do this. ... and to certain higher rank groups. This is because our counting argument for general lattices is elementary and highly flexible, and should generalise to ... gerris closet facebook uniontown ohioWebJan 1, 2015 · Counting arithmetic lattices and surfaces Article Full-text available Nov 2008 ANN MATH Mikhail Belolipetsky Tsachik Gelander Alexander Lubotzky Aner Shalev We give estimates on the number... christmas events in ipswich