Complexity amongst the finitely generated subgroups of Thompson's Group

This project is aimed at exploring the structure of groups (and of subgroups of groups) in the generalised R. Thompson family of groups, under various complexity constraints. The generalised R. Thompson family of groups represents an important class of groups, where the theory of these groups often has connections and applications to/in various areas of mathematics including topology, analysis, logic, and dynamics.

The complexity constraints we have in mind are of various types: E.g., exploring the structure of the elementary amenable subgroups of R. Thompson group F, exploring groups or subgroups under growth conditions for counting group elements, considering the subgroup structure of those subgroups of R. Thompson's groups T or V which contain no non-abelian free subgroups, understanding commutator width in any of the R. Thompson groups or their generalisations, deciding if the boundary groups for Thurston's Piecewise Integral Projective groups (natural generalisations of R. Thompson's group T) are finitely generated or not, and etc.

SMSTC courses; ID5101; school seminars