Simple groups without lattices

Bader, Uri;Caprace, Pierre-Emmanuel;Gelander, Tsachik;Mozes, Shahar
(2012) Bulletin of the London mathematical society — Vol. 44, n° 1, p. 55-67 (2012)

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We show that the group of almost automorphisms of a d-regular tree does not admit lattices. As far as we know, this is the first such example among (compactly generated) simple locally compact groups.
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Bader, U., Caprace, P.-E., Gelander, T., & Mozes, S. (2012). Simple groups without lattices. Bulletin of the London mathematical society, 44(1), 55-67. https://doi.org/10.1112/blms/bdr061 (Original work published 2012)