Owen Baker, McMaster University
“Hyperbolic Group Boundaries and Cannon-Thurston Maps”
Gromov defined a class of groups called hyperbolic groups and associated a boundary space to each. A natural question arises: if H¡G are hyperbolic groups, does inclusion induce a map from the boundary of H to that of G? Such a map, when well-defined, is called a Cannon-Thurston map after a family of examples constructed by Cannon and Thurston. In this talk, I will discuss joint work with Tim Riley where we answer the question in the negative. Time permitting, I will talk about connections with subgroup distortion.