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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> > 6.</p>