On property (T) for \(\Aut(F_n)\) and \(\mathrm{SL}_n(\mathbb{Z})\)

DOI10.4007/annals.2021.193.2.3zbMath1483.22006arXiv1812.03456OpenAlexW3135129921MaRDI QIDQ2662017

Marek Kaluba, Piotr W. Nowak, Dawid Kielak

Publication date: 8 April 2021

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.03456

zbMATH Keywords

automorphism groups of free groupsKazhdan constantsspectral gapsKazhdan's property (T)

Mathematics Subject Classification ID

Automorphism groups of groups (20F28) Kazhdan's property (T), the Haagerup property, and generalizations (22D55)

Related Items

Interview with Igor Pak, On representations of \(\operatorname{Gal}(\overline{\mathbb{Q}} / \mathbb{Q})\), \(\widehat{GT}\) and \(\operatorname{Aut}(\hat{F}_2)\), \(C^1\) actions on the circle of finite index subgroups of \(\mathrm{Mod}(\Sigma_g)\), \(\mathrm{Aut}(F_n)\), and \(\mathrm{Out}(F_n)\), Żuk’s criterion for Banach spaces and random groups, Tame automorphism groups of polynomial rings with property (T) and infinitely many alternating group quotients, Arithmetic and dynamics on varieties of Markoff type, Geometric structures in group theory. Abstracts from the workshop held February 27 -- March 5, 2022, Arithmetic quotients of the automorphism group of a right-angled Artin group, Maximal subgroups and von Neumann subalgebras with the Haagerup property, Outer automorphism groups of right-angled Coxeter groups are either large or virtually abelian, \(\Aut(\mathbb{F}_5)\) has property \((T)\)

Uses Software

• GAP
• Julia
• JuMP
• SCS
• Hecke
• Nemo

Cites Work

• Conic optimization via operator splitting and homogeneous self-dual embedding
• Linear representations of the automorphism group of a free group.
• Certifying numerical estimates of spectral gaps
• \(\Aut(\mathbb{F}_5)\) has property \((T)\)
• The product replacement algorithm and Kazhdan’s property (T)
• Kazhdan’s Property (T) via Semidefinite Optimization
• Julia: A Fresh Approach to Numerical Computing
• A faithful polynomial representation of Out F₃
• KAZHDAN CONSTANTS FOR SL_n(ℤ)
• NONCOMMUTATIVE REAL ALGEBRAIC GEOMETRY OF KAZHDAN’S PROPERTY (T)
• [https://portal.mardi4nfdi.de/wiki/Publication:3695463 Aut(F) →Aut(F/F � � ) is Surjective for Free Group F of Rank 4]
• The Nonfinite Generation of Aut(G), G Free metabelian of Rank 3
• Finite Quotients of the Automorphism Group of a Free Group
• Generating random elements of a finite group
• Nemo/Hecke
• Computing Kazhdan Constants by Semidefinite Programming
• JuMP: A Modeling Language for Mathematical Optimization
• Bounded generation and Kazhdan's property (T)
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item