$\mathrm{Aut}({\mathbb{F}}_5)$ has property $(T)$

Abstract

We give a constructive, computer-assisted proof that $\mathrm{Aut}({\mathbb{F}}_5)$, the automorphism group of the free group on $5$ generators, has Kazhdan's property $(T)$.

link to the code is provided within the article; v2 improved exposition, corrected typos

References in corpus (1)

• JuMP: A Modeling Language for Mathematical Optimization

Cited by in corpus (5)

• A substitute for Kazhdan's property (T) for universal non-lattices
• On the Ground State Energies of Discrete and Semiclassical Schrödinger Operators
• On representations of $\mathrm{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$, $\widehat{GT}$ and $\mathrm{Aut}({\hat{F}}_2)$
• Non-vanishing unitary cohomology of low-rank integral special linear groups
• The space of non-extendable quasimorphisms