EVENT DETAILS AND ABSTRACT

Title: Finitely presented groups associated with expanding maps
Speaker: Volodymyr Nekrashevych
Speaker Info: Texas A&M University
Brief Description:
Special Note: the reading seminar will be replaced by this talk. Joint with algebra seminar.
Abstract:

We associate with every locally expanding map $f:X\to X$ of a compact metric space $X$ a group $V_f$. This group is generated by a copy of the iterated monodromy group and the Higman-Thompson group. But unlike the iterated monodromy group, the group $V_f$ is finitely presented. Moreover, it is a complete invariant of the dynamical systems. If $f_1$ and $f_2$ are locally expanding maps of compact path connected spaces, then $V_{f_1}$ and $V_{f_2}$ are isomorphic as abstract groups if and only if the dynamical systems are topologically conjugate. I will discuss the main ideas of the proof of this fact and some possible generalizations.