The Further Chameleon Groups of Richard Thompson and Graham Higman: Autohisms via Dynamics for the Higman-Thompson Groups $G_{n,r}$

C. Bleak, University of St. Andrews, Scotland, United Kingdom. P. Cameron, University of St. Andrews, Scotland, United Kingdom. Y. Maissel, Ben-Gurion University of the Negev, Beer-Sheva, Israel. A. Navas, University of Santiago de Chile, Chile. F. Olukoya, University of St. Andrews, Scotland, United Kingdom.

1. Introduction 2. Language, notation, and groups 3. More on $G_{n,r,\mathrm {d}}$, $G_{n,r,\mathrm {p}}$, $G_{n,r}$, and $H_{n,r,{\sim }}$ 4. Local actions 5. On the rational group $\mathcal {R}_n$ and the related groups $\mathcal {R}_{n,r}$ 6. Automorphisms admit few local actions 7. Finding our place in the rational group $\mathcal {R}_{n,r}$ 8. Combinatorial properties of strongly synchronizing transducers 9. The natural quotient $\mathcal {B}_{n,r}\twoheadrightarrow \mathcal {O}_{n,r}$ 10. Root functions and detecting flavours of synchronicity 11. Open problems A. The inversion construction