\text Aut(\mathbb F₅) has property (T)

2017/12/31 by Marek Kaluba, Piotr W. Nowak, Narutaka Ozawa
Mathematics · #Advanced Operator Algebra Research #Automorphism #Automorphism group #Free group #Geometric and Algebraic Topology #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Inner automorphism #Property (philosophy) #math.FA #math.GR #math.OA

paper · pdf · doi:10.1007/s00208-019-01874-9

published as Math. Ann. 375 (2019) 1169-1191 · link to the code is provided within the article; v2 improved exposition, corrected typos

openalex created_date 2018/01/05 · arxiv created 2019/03/22 · openalex publication_date 2019/08/08 · arxiv updated 2021/01/21 · openalex updated_date 2026/08/05

Abstract

We give a constructive, computer-assisted proof that \text Aut(\mathbb F₅) , the automorphism group of the free group on 5 generators, has Kazhdan’s property (T).

Citations

• Linear Representations of Finite Groups
• Automorphism groups of free groups, surface groups and free abelian groups
• NONCOMMUTATIVE REAL ALGEBRAIC GEOMETRY OF KAZHDAN’S PROPERTY (T)
• Julia: A Fresh Approach to Numerical Computing