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September 10, 2025

Arboreal Galois groups of postcritically finite quadratic polynomials: The periodic case

Key Points

The study explicitly constructs the arboreal galois group associated with certain polynomials.
Focusing on periodic critical points, the findings reveal intricate structures within quadratic polynomials.
An arbitrary field of characteristic not equal to 2 serves as the foundation for the applicable case analysis.
This approach may lead to deeper insights into the dynamics of postcritically finite systems.

Abstract

Abstract We provide an explicit construction of the arboreal Galois group for the postcritically finite polynomial , where 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.

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Cite This Study

Benedetto et al. (Fri,) studied this question.

synapsesocial.com/papers/68c1aacc54b1d3bfb60e345d https://doi.org/https://doi.org/10.1112/jlms.70257

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