Departmental Colloquium
Volodymyr Nekrashevych
Texas A&M University
Hyperbolic groupoids
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.
Friday March 11, 2011 at 3:00 PM in SEO 636