Complexity amongst the finitely generated subgroups of Thompson's Group

这个项目的目的是探索在各种复杂性约束下，广义R.Thompson群族中的群(及其子群)的结构。广义R.Thompson群族代表了一类重要的群，其中这些群的理论经常与包括拓扑学、分析、逻辑和动力学在内的数学的各个领域有联系和应用。我们考虑的复杂性约束是各种类型的：例如，探索R.Thompson群F的初等从属子群的结构，探索增长条件下的群或子群以计数群元素，考虑不包含非交换自由子群的R.Thompson群T或V的子群的子群结构，理解任何R.Thompson群或它们的推广中的交换子宽度，确定瑟斯顿逐段积分射影群(R.Thompson群T的自然推广)的边界群是否有限生成等SMSTC过程；ID5101；学校研讨会

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