On property (T) for Aut(F_n) and SL_n(ℤ)

2018/12/09 by Marek Kaluba, Dawid Kielak, Kaluba, Marek +3 · 1 citation
Mathematics · #Advanced Topology and Set Theory #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1812.03456

Abstract

We prove that Aut(F_n) has Kazhdan's property (T) for every n \geqslant 6. Together with a previous result of Kaluba, Nowak, and Ozawa, this gives the same statement for n\geqslant 5. We also provide explicit lower bounds for the Kazhdan constants of SAut(F_n) (with n \geqslant 6) and of SL_n(ℤ) (with n \geqslant 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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