Hyperbolic Coxeter groups of large dimension

Hyperbolic Coxeter groups of large dimension
复制标题

大维双曲 Coxeter 群

DOI：
--
复制
发表时间：
2003
期刊：
影响因子：
--
通讯作者：
J. Świa̧tkowski
J. Świa̧tkowski
中科院分区：
--
文献类型：
--
作者：
T. Januszkiewicz;J. Świa̧tkowski

文献摘要

被引文献

相似文献

摘要我们构造了Gromov双曲的例子 任意大维的Coxeter群。 我们还推广了Vinberg定理，证明了如果一个Gromov 双曲Coxeter群是一个虚拟Poincaré对偶群 在维度n中， 然后n≤61.作用于其相关络合物的Coxeter基团已经非常 有用的例子来源和对非正曲线空间的洞察 在过去几年里。负曲线(或格罗莫夫双曲线) 科克塞特小组则更加难以捉摸。尤其是它们存在于 高维是值得怀疑的。1987年，Gabor MousSong[M]猜想 任意Gromov双曲Coxeter群的虚拟上同调维数。 米莎·格罗莫夫[G]也提出了这个问题(他认为或许 任何高维负曲空间的构造都需要 本质算术群伪装下的非平凡数论 Way)和Mladen Bestvina[B2].在本文中我们证明了高维Gromov双曲Coxeter 群确实存在，我们用几何或群论来构造它们，但是 不是算术平均值。
AbstractWe construct examples of Gromov hyperbolic Coxeter groups of arbitrarily large dimension. We also extend Vinberg’s theorem to show that if a Gromov hyperbolic Coxeter group is a virtual Poincaré duality group of dimension n, then n ≤ 61.Coxeter groups acting on their associated complexes have been extremely useful source of examples and insight into nonpositively curved spaces over last several years. Negatively curved (or Gromov hyperbolic) Coxeter groups were much more elusive. In particular their existence in high dimensions was in doubt.In 1987 Gabor Moussong [M] conjectured that there is a universal bound on the virtual cohomological dimension of any Gromov hyperbolic Coxeter group. This question was also raised by Misha Gromov [G] (who thought that perhaps any construction of high dimensional negatively curved spaces requires nontrivial number theory in the guise of arithmetic groups in an essential way), and by Mladen Bestvina [B2].In the present paper we show that high dimensional Gromov hyperbolic Coxeter groups do exist, and we construct them by geometric or group theoretic but not arithmetic means.