• Media type: E-Article
  • Title: On property (T) for Aut(Fn ) and SL n (ℤ)
  • Contributor: Kaluba, Marek; Kielak, Dawid; Nowak, Piotr W.
  • Published: Annals of Mathematics, 2021
  • Published in: Annals of Mathematics, 193 (2021) 2, Seite 539-562
  • Language: English
  • DOI: 10.4007/annals.2021.193.2.3
  • ISSN: 0003-486X; 1939-8980
  • Origination:
  • Footnote:
  • Description: <p>We prove that Aut(<italic>F<sub>n</sub> </italic>) has Kazhdan's property (T) for every <italic>n</italic> ⩾ 6. Together with a previous result of Kaluba, Nowak, and Ozawa, this gives the same statement for <italic>n</italic> ⩾ 5. We also provide explicit lower bounds for the Kazhdan constants of SAut(<italic>F<sub>n</sub> </italic>) (with <italic>n</italic> ⩾ 6) and of SL<sub> <italic>n</italic> </sub>(ℤ) (with <italic>n</italic> ⩾ 3) with respect to natural generating sets. In the latter case, these bounds improve upon previously known lower bounds whenever <italic>n</italic> &gt; 6.</p>