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.