Geometry and Analysis on Groups Research Seminar

"Geometry and Analysis on Groups" Research Seminar

Time: 2018.06.12, 15:00–17:00
Location: Seminarraum 10, Oskar-Morgenstern-Platz 1, 2.Stock
Title: "Subgroups of Thompson's group."
Speaker: Justin Moore (Cornell University)
Abstract: Matthew Brin and Mark Sapir have conjectured that every subgroup of Thompson's group \(F\) is either elementary amenable or else contains an isomorphic copy of \(F\). We hope to address this question by attempting to classify - or at least better understand - the class of all finitely generated subgroups of \(F\) up to biembeddability. In particular, it seems necessary to obtain a more complete understanding of the elementary amenable subgroups of \(F\) before attempting to prove the Brin-Sapir conjecture. We will show that there is a family of finitely generated elementary amenable subgroups of \(F\) which is strictly well ordered in type \(\epsilon_0\) by the embeddability relation. Moreover, we show that the EA-class of a finitely generated subgroup of \(F\) can be made arbitrarily large below \(\epsilon_0\), improving on previous results of Brin. The work presented in this talk is joint with Collin Bleak and Matthew Brin.

The first lecture will develop a language which allows us to specify certain subgroups of Thompson's group. The second lecture will focus on the construction of the specific family of examples mentioned above.