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arXiv · 1804.06053

Arboreal representations for rational maps with few critical points

Jamie Juul·Holly Krieger·Nicole Looper·Michelle Manes·Bianca Thompson·Laura Walton
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Abstract

Jones conjectures the arboreal representation of a degree two rational map will have finite index in the full automorphism group of a binary rooted tree except under certain conditions. We prove a version of Jones' Conjecture for quadratic and cubic polynomials assuming the $abc$-Conjecture and Vojta's Conjecture. We also exhibit a family of degree $2$ rational maps and give examples of degree $3$ polynomial maps whose arboreal representations have finite index in the appropriate group of tree automorphisms.

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Jamie Juul, Holly Krieger, Nicole Looper, Michelle Manes, Bianca Thompson, Laura Walton. 2018-04-18. Arboreal representations for rational maps with few critical points. https://arxiv.org/abs/1804.06053

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