Texas A&M University, Department of
Mathematics, 216 Milner Hall, 1st of February 2006, 3:00-3:50
Groups and Dynamics Seminar
A minimal Cantor
set in the space of 3-generated groups
Volodymyr Nekrashevych of Texas A&M
University
We will discuss a self-similar uncountable family of groups D_w
parametrized by infinite binary sequences. This family is homeomorphic
to the Cantor set with respect to a natural topology on the space of
(marked)
3-generated groups.
We will also show that this set is minimal, i.e., that it has dense
isomorphism classes, giving a complete classification of the groups D_w
up to isomorphisms.
A relation to a Thurston's theorem on topological polynomials will be
eventually described.