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Réseaux de Coxeter-Davis et commensurateurs

Frédéric Haglund — 1998

Annales de l'institut Fourier

For each integer $k \geq 6$ and each finite graph $L$ , we construct a Coxeter group $W$ and a non positively curved polygonal complex $A$ on which $W$ acts properly cocompactly, such that each polygon of $A$ has $k$ edges, and the link of each vertex of $A$ is isomorphic to $L$ . If $L$ is a “generalized $m$ -gon”, then $A$ is a Tits building modelled on a reflection group of the hyperbolic plane. We give a condition on $Aut (L)$ for $Aut (A)$ to be non enumerable (which is satisfied if $L$ is a thick classical generalized $m$ -gon). On the other hand,...

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