Spaces and groups with conformal dimension greater than one
by
John Mackay
University of Michigan

The conformal dimension of a metric space is a quasisymmetric invariant that in some sense measures the `best shape' of the metric space under quasisymmetric deformations. In this talk I'll survey some known results about conformal dimension and give examples where this invariant is interesting, such as the boundary at infinity of a Gromov hyperbolic group, paying particular attention to spaces of topological dimension one. I'll also describe recent work that gives a lower bound greater than one for a natural class of metric spaces that includes boundaries of hyperbolic groups that are connected with no local cut points.

Paper reference: arXiv:0711.0417

Date received: January 23, 2008