Quasi-hyperbolic planes in hyperbolic and relatively hyperbolic groups

Quasi-hyperbolic planes in hyperbolic and relatively hyperbolic groups

Mon, 11/02
15:45 		John MacKay (Oxford) Topology Seminar Add to calendar L3
Quasi-hyperbolic planes in hyperbolic and relatively hyperbolic groups
In 2005, Bonk and Kleiner showed that a hyperbolic group admits a quasi-isometrically embedded copy of the hyperbolic plane if and only if the group is not virtually free. This answered a question of Papasoglu. I will discuss a generalisation of their result to certain relatively hyperbolic groups (joint work with Alessandro Sisto). Key tools involved are new existence results for quasi-circles, and a better understanding of the geometry of boundaries of relatively hyperbolic groups.