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New Kazhdan groups

Jan Dymara·Tadeusz Januszkiewicz
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Abstract

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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Jan Dymara, Tadeusz Januszkiewicz. 1999-05-05. New Kazhdan groups. https://arxiv.org/abs/math/9905025

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