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arXiv · 2412.03313

Arboreal Galois groups of rational maps with nonreal Julia sets

Chifan Leung
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Abstract

We prove a non-abelian arboreal Galois group result for certain maps with non-real Julia set at an archimedean place. We investigate the question of determining which polynomials defined over $\mathbb{R}$ have real Julia set. Finally we show that for some certain classes of Latt\`es maps associated to the duplication map on an elliptic curve has non-abelian arboreal Galois groups.

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Chifan Leung. 2024-12-04. Arboreal Galois groups of rational maps with nonreal Julia sets. https://arxiv.org/abs/2412.03313

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