Topology and Geometric Group Theory Seminar

Tim RileyCornell University
Fractional distortion in hyperbolic groups

Thursday, September 1, 2022 - 2:45pm
Malott 206

Distortion concerns how an intrinsic metric on a subspace differs from a metric on the ambient space. In the context of groups, it compares a subgroup's word metric with that of the group in which it sits.

Groups that are hyperbolic have the defining feature that geodesic triangles in their Cayley graphs are uniformly thin. The tree-like nature of this condition might suggest that distortion does not occur within hyperbolic groups. However, I will exhibit hyperbolic groups with subgroups displaying a full spectrum of distortion behaviours. More precisely, I will show that for all integers p > q > 0, there is a hyperbolic group with a subgroup whose distortion function grows like exp(n^{p/q}).

This work is with Pallavi Dani.