An automata theoretic proof that $\mathop{\mathrm{Out}}(T) \cong \mathbb{Z}/2\mathbb{Z}$ and some embedding results for $\mathop{\mathrm{Out}}(V)$
Year: 2020
Type: preprint
Abstract: In a seminal paper, Brin demonstrates that the outerautomorphism group of Thompson group $T$ is isomorphic to the cyclic group of order two. In this article, building on characterisation of automorphisms of the Higman-Thompson groups $G_{n,r}$ and $T_{n,r}$ as groups of transducers, we give a new proof, automata theoretic in nature, of Brin's result. We also demonstrate that the group of outerautomorphisms of Thompson's group $V = G_{2,1}$ contains an isomorphic copy of Thompson's group $F$. This extends a result of the author demonstrating that whenever $n \ge 3$ and $1 \le r < n$ the outerautomorphism groups of $G_{n,r}$ and $T_{n,r}$ contain an isomorphic copy of $F$.
Source: arXiv (Cornell University)
Author: Olukoya, Feyishayo
Institution: University of Aberdeen
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G8631404110
OpenAlex ID: W3015004548