Volodymyr Nekrashevych : Hyperbolic groupoids

Posted by Emily Dumas , part of the Departmental Colloquium.

At

March 11, 2011, 3 p.m.

In

SEO 636

Abstract

We will define a notion of a hyperbolic groupoid (or a pseudogroup) which includes as partial cases actions of Gromov hyperbolic groups on their boundaries, pseudogroups generated by hyperbolic complex rational functions, one-sided shifts of finite type, and groupoids naturally associated with Anosov diffeomorphisms. For every hyperbolic groupoid G a naturally defined dual groupoid G' acts on the boundary of the Cayley graphs of G. The dual groupoid G' is also hyperbolic and G'' is equivalent to G. Different examples of pairs of mutually dual groupoids, and some applications of the duality theorem will be described.