Chris Karpinski, McGill University
Relativizing computable categoricity
A metric space is hyperbolic if geodesic triangles in the metric space are uniformly slim. To any hyperbolic metric space, one can associate a boundary at infinity, a topological space called the Gromov boundary. A group acting on a hyperbolic metric space by isometries induces an action on the associated Gromov boundary by homeomorphisms. Given a hyperbolic space equipped with an action of a group, one can then study the orbit equivalence relation of the boundary action. We show that a class of groups of interest in geometric group theory, defined using graphical small cancellation theory, induce hyperfinite orbit equivalence relations on the boundaries of their natural hyperbolic Cayley graphs, meaning roughly that the orbits look like lines. This is joint work with Damian Osajda and Koichi Oyakawa.
MC 5403