JournalsggdVol. 7, No. 1pp. 39–107

Combinatorial modulus, the combinatorial Loewner property, and Coxeter groups

  • Marc Bourdon

    Université Lille I, Villeneuve d'Ascq, France
  • Bruce Kleiner

    Courant Institute of Mathematical Sciences, New York, United States
Combinatorial modulus, the combinatorial Loewner property, and Coxeter groups cover
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Abstract

We study combinatorial modulus on self-similar metric spaces. We give new examples of hyperbolic groups whose boundaries satisfy a combinatorial version of the Loewner property, and prove Cannon’s conjecture for Coxeter groups. We also establish some connections with p\ell_p-cohomology.

Cite this article

Marc Bourdon, Bruce Kleiner, Combinatorial modulus, the combinatorial Loewner property, and Coxeter groups. Groups Geom. Dyn. 7 (2013), no. 1, pp. 39–107

DOI 10.4171/GGD/177