Events for 03/08/2023 from all calendars

Groups and Dynamics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Yaroslav Vorobets

Title: Maximal subgroups of ample (topological full) groups

Abstract: Given a group of homeomorphisms of the Cantor set, usually there are many ways to construct a new homeomorphism, as a puzzle, from pieces of several given ones. The group is called ample (or topological full) if it already contains all homeomorphisms obtained that way. The talk is concerned with the first attempt at a classification of maximal subgroups of ample groups. Results that will be presented are mostly parallel to the classification of maximal subgroups of finite symmetric groups. Recall that all subgroups of the symmetric group are divided into three classes: intransitive subgroups (those that leave invariant a nontrivial subset), imprimitive subgroups (transitive subgroups that leave invariant a nontrivial partition), and primitive subgroups (the remaining ones). It turns out that the maximal intransitive subgroups are stabilizers of certain subsets while the maximal imprimitive subgroups are stabilizers of certain partitions. In the case of the ample groups, arbitrary subsets and partitions are replaced by closed subsets and partitions into closed subsets. Transitivity is replaced by minimality (absence of nontrivial closed invariant subsets). This is the joint work with Rostislav Grigorchuk.