The boundary of a Gromov hyperbolic group carries a canonical family of metrics which determine the quasi-isometry type of the group. Pansu’s conformal dimension of the boundary gives a natural and important quasi-isometric invariant. I will discuss how this invariant behaves when the group splits over two-ended subgroups (i.e. when the boundary has local cut points), and applications to the question of Bonk and Kleiner asking for a characterization of when this dimension equals one.
Joint work with Matias Carrasco.
This video is part of the New York Group Theory Cooperative‘s group theory seminar series.
