On property (T) for Aut(Fn) and SLn(Z)

• 成果类型: Article
• 署名作者: Kaluba, Marek; Kielak, Dawid; Nowak, Piotr W.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2021.193.2.3
• 发表日期: 2021
• 页码: 539-562
• 关键词: automorphism group; kazhdan constants; generation

摘要

We prove that Aut(F-n) has Kazhdan's property (T) for every n >= 6. Together with a previous result of Kaluba, Nowak, and Ozawa, this gives the same statement for n >= 5. We also provide explicit lower bounds for the Kazhdan constants of SAut(F-n) (with n >= 6) and of SLn (Z) (with n >= 3) with respect to natural generating sets. In the latter case, these bounds improve upon previously known lower bounds whenever n > 6.