Abstract
The group of simplicial automorphisms of a Tits–Kac–Moody infinite building of thickness q associated to a cocompact reflexion group with fundamental domain a simplex, is Kazhdan for q sufficiently large. Thus we obtain families of new Kazhdan groups: two in dimension 3 and one in dimension 4. The proof uses continuous cohomology, in particular a lemma of Casselman–Wigner, and Garland's vanishing method.
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Dymara, J., Januszkiewicz, T. New Kazhdan Groups. Geometriae Dedicata 80, 311–317 (2000). https://doi.org/10.1023/A:1005255003263
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DOI: https://doi.org/10.1023/A:1005255003263