Arboreal Galois groups of postcritically finite quadratic polynomials

Robert L. Benedetto, Dragos Ghioca, Jamie Juul, Thomas J. Tucker

Published 2024-11-11Version 1

We provide an explicit construction of the arboreal Galois group for the postcritically finite polynomial $f(z) = z^2 +c$, where $c$ belongs to some arbitrary field of characteristic not equal to $2$. In this first of two papers, we consider the case that the critical point is periodic.