Brita Nucinkis

Description

Title: An irrational slope Thompson's group

Abstract:
In this talk I will discuss a relative to Thompson's group $F$, the group $F_\tau,$ which is the group of piecewise linear homeomorphisms of $[0,1]$ with breakpoints in $\mathbb{Z}[\tau]$ and slopes powers of $\tau,$ where $\tau = \frac{\sqrt5 -1}{2}$ is the small Golden Ratio. This group was first considered by S. Cleary, who showed that the group was finitely presented and of type $\operatorname{F}_\infty.$ Here we take a combinatorial approach considering elements as tree-pair diagrams, where the trees are finite binary trees, but with two different kinds of carets. We use this representation to show that the commutator subgroup is simple, give a unique normal form, and study some metric properties of this group. This is joint work with J. Burillo and L. Reeves.

Period	25 Feb 2019
Visiting from	Royal Holloway, University of London (United Kingdom)
Visitor degree	PhD
Degree of Recognition	Local