Quasi-möbius maps of Morse boundaries

Vortrag von Dr. Matthew Cordes

Datum: 26.09.18  Zeit: 15.45 - 16.45  Raum: ETH HG G 43

Boundaries of hyperbolic groups can tell you a great deal about the group. For instance, one can show two groups are not quasi-isometric by showing their boundaries are not homeomorphic. Paulin showed that under the right conditions you can show that two groups with homeomorphic boundaries are quasi-isometric. By restricting to rays satisfying the Morse property, one can define an analogous boundary for more general groups. Inspired by the theorem of Paulin, we give precise conditions for when a homeomorphism between the Morse boundaries of two groups is induced by a quasi-isometry of the groups themselves. This is joint work with Ruth Charney and Devin Murray.