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Réseaux de Coxeter-Davis et commensurateurs

Frédéric Haglund (1998)

Annales de l'institut Fourier

For each integer k 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,...

R-trees and the Bieri-Neumann-Strebel invariant.

Gilbert Levitt (1994)

Publicacions Matemàtiques

Let G be a finitely generated group. We give a new characterization of its Bieri-Neumann-Strebel invariant Σ(G), in terms of geometric abelian actions on R-trees. We provide a proof of Brown's characterization of Σ(G) by exceptional abelian actions of G, using geometric methods.

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