New Kazhdan groups

Details New Kazhdan groups New Kazhdan groups

1999-05-05

arxiv.org/abs/math/9905025v1

Geom. Dedicata 80 (2000), no. 3, 311-317

Mathematics

Group Theory

7 pages, TeX

Scientific paper

The group of simplicial automorphisms of a Tits-Kac-Moody ininite 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 continuos cohomology, in particular a lemma of Borel-Wallach, and Garland's vanishing method.

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