16 papers
Corrigendum and addendum to "Fixed-point-free elements of iterated monodromy groups" [Trans. of the American Mathematical Society Vol. 367, No. 3 (2015), 2023-2049]
Jorge Fariña-Asategui, Rafe Jones, Santiago Radi
In this note we document a gap in an argument in the above paper, and point to new work in the literature giving a complete proof of the main result.
Arboreal Galois representations of rational functions: fixed-point proportion and the extension problem
Jorge Fariña-Asategui
We give an explicit description of the arithmetic-geometric extension of iterated Galois groups of rational functions. This yields a complete solution to the extension problem when…
Virtual retracts in groups acting on rooted trees
Jorge Fariña-Asategui, Jon Merladet Urigüen
We study virtual retracts in groups acting on rooted trees. We show that finitely generated branch groups do not have the local retraction (LR) property. Furthermore, we specialize…
Fixed-point proportion of geometric iterated Galois groups
Jorge Fariña-Asategui, Santiago Radi
In 1980, Odoni initiated the study of the fixed-point proportion of iterated Galois groups of polynomials motivated by prime density problems in arithmetic dynamics. The main goal…
Non-closed subgroups of weakly branch groups
Jorge Fariña-Asategui, Paul-Henry Leemann, Tatiana Nagnibeda
For a weakly branch group acting on a regular enough rooted tree, we provide two constructions of continuous families of distinct subgroups that are not closed in the profinite…
Random subgroups of branch groups
Jorge Fariña-Asategui, Santiago Radi
We show that independent Haar-random elements in a super strongly fractal branch profinite group generate a free subgroup acting freely on the boundary of the tree. This improves a…