Quasi-hyperbolic planes in hyperbolic and relatively hyperbolic groups

Seminar series

Date

Mon, 11 Feb 2013

Time

15:45 - 16:45

Location

Speaker

John MacKay

Organisation

Oxford

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.