Conformal dimension and canonical splittings of hyperbolic groups

Matias Carrasco Piaggio (1)

1 Topologie et Dynamique

We prove a general criterion for a metric space to have conformal dimension one. The conditions are stated in terms of the existence of enough local cut points in the space. We then apply this criterion to the boundaries of hyperbolic groups and show an interesting relationship between conformal dimension and some canonical splittings of the group.

Mots clés: canonical splittings; conformal dimension; local cut points; Gromov-hyperbolic groups; canonical splittings.

Domaines: Géométrie métrique [math.MG]; Théorie des groupes [math.GR]

Matias Carrasco Piaggio. Conformal dimension and canonical splittings of hyperbolic groups. 2013. ⟨hal-00781575v4⟩