Universal lattices and property tau

• 成果类型: Article
• 署名作者: Kassabov, Martin; Nikolov, Nikolay
• 署名单位: Cornell University; University of Oxford
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-005-0498-0
• 发表日期: 2006
• 页码: 209-224
• 关键词: kazhdan constants; k2

摘要

We prove that the universal lattices - the groups G = SLd(R) where R = Z[x(1),..., x(k)], have property tau for d >= 3. This provides the first example of linear groups with t which do not come from arithmetic groups. We also give a lower bound for the tau-constant with respect to the natural generating set of G. Our methods are based on bounded elementary generation of the finite congruence images of G, a generalization of a result by Dennis and Stein on K-2 of some finite commutative rings and a relative property T of (SL2( R) x R-2, R-2).