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arXiv · 2507.08347

Arboreal Galois groups of postcritically finite quadratic polynomials: The strictly preperiodic case

Robert L. Benedetto·Dragos Ghioca·Jamie Juul·Thomas J. Tucker
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Abstract

In a previous paper, we provided an explicit description of the arboreal Galois group of the postcritically finite polynomial $f(z) = z^2 +c$ in the special case when the critical point $0$ is periodic under the action of $f(z)$. In the current paper, we complete the picture for all postcritically finite polynomials by addressing the cases when $0$ is strictly preperiodic for the polynomial $f(z)$.

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Robert L. Benedetto, Dragos Ghioca, Jamie Juul, Thomas J. Tucker. 2025-07-11. Arboreal Galois groups of postcritically finite quadratic polynomials: The strictly preperiodic case. https://doi.org/10.4153/s0008414x2610217x

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