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

preprint2019arXivOpen access

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

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

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Aut⁡(F5)\operatorname{Aut}(\mathbb{F}_5)Aut(F5​) has property (T)(T)(T)

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