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.