Papers › On property (T) for Aut(Fₙ) and SLₙ(ℤ)
On property (T) for Aut(Fₙ) and SLₙ(ℤ)
Marek Kaluba, Dawid Kielak, Piotr W. Nowak
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We prove that Aut(Fₙ) 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(Fₙ) (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.
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