Menger Curve Boundaries of Hyperbolic Quotients
Date:
The Menger curve comes up naturally when discussing boundaries of hyperbolic groups. In this talk, we will introduce boundaries of hyperbolic groups and the structure of Menger curve boundaries. We will look at what happens to these boundaries under quotients, while focusing on an important property of the Menger curve, which is that it is not embeddable in the sphere (non-planar). We will see that the key to understanding these quotient boundaries is to find a non-planar graph in them.