Iterated monodromy group of a PCF quadratic non-polynomial map

Abstract

We study the postcritically finite non-polynomial map f(x)=1(x-1)2 over a number field k and prove various results about the geometric Ggeom(f) and arithmetic Garith(f) iterated monodromy groups of f. We show that the elements of Ggeom(f) are the ones in Garith(f) that fix certain roots of unity by assuming a conjecture on the size of G<inf>n</inf>geom(f). Furthermore, we describe exactly for which a∈k the Arboreal Galois group G<inf>a</inf>(f) and Garith(f) are equal. © 2024 Elsevier B.V., All rights reserved.