Filling boundaries of coarse manifolds in semisimple and solvable arithmetic groups
Filling boundaries of coarse manifolds in semisimple and solvable arithmetic groups
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半简单可解算术群中粗流形的边界填充
DOI：
10.4171/jems/419
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发表时间：
2011
影响因子：
2.6
通讯作者：
Kevin A. Wortman
中科院分区：
文献类型：
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作者：
M. Bestvina;A. Eskin;Kevin A. Wortman
我们提供了部分结果对算术群（在数域或函数域）的Lubotzky-Mozes-Raghunathan定理的代数推广，这意味着，在低维，多项式等周不等式和有限性。作为证明的工具，我们建立了多项式等周不等式和有限性的某些可解群，出现在半单群的抛物群的子群，从而推广了Bux定理。我们还开发了一个精确的版本的减少理论的算术组的证明是，在大多数情况下，独立的基本全球领域是否是一个数字字段或功能字段。我们的主要结果是下面的定理4。在陈述之前，我们提供一些背景。0.1.算术组。设K是一个整体域（数域或函数域），S是K的n个不等赋值的非空集合，每个不等赋值类都有一个。环OS K将表示相应的S-整数环。对任意v ∈ S，设Kv是K关于v的完备化，使得Kv是局部紧域。设G是一个非交换的、绝对几乎单的、K-迷向的K-群。设G是半单李群
We provide partial results towards a conjectural generalization of a theorem of Lubotzky-Mozes-Raghunathan for arithmetic groups (over number fields or function fields) that implies, in low dimensions, both polynomial isoperimetric inequalities and finiteness properties. As a tool in our proof, we establish polynomial isoperimetric inequalities and finiteness properties for certain solvable groups that appear as subgroups of parabolic groups in semisimple groups, thus generalizing a theorem of Bux. We also develop a precise version of reduction theory for arithmetic groups whose proof is, for the most part, independent of whether the underlying global field is a number field or a function field. Our main result is Theorem 4 below. Before stating it, we provide some background. 0.1. Arithmetic groups. Let K be a global field (number field or function field), and let S be a nonempty set of finitely many inequivalent valuations of K including one from each class of archimedean valuations. The ring OS ⊆ K will denote the corresponding ring of S-integers. For any v ∈ S, we let Kv be the completion of K with respect to v so that Kv is a locally compact field. Let G be a noncommutative, absolutely almost simple, K-isotropic K-group. Let G be the semisimple Lie group
正特征还原算术群的更高有限性：秩定理
影响因子：
4.9
作者：
Kai-Uwe Bux;Ralf Köhl;Stefan Witzel
通讯作者：
Stefan Witzel