A large arboreal Galois representation for a cubic postcritically finite polynomial

@article{Benedetto2016ALA,
  title={A large arboreal Galois representation for a cubic postcritically finite polynomial},
  author={Robert L. Benedetto and X. W. C. Faber and Benjamin Hutz and Jamie Juul and Yu Yasufuku},
  journal={Research in Number Theory},
  year={2016},
  volume={3},
  pages={1-21}
}
We give a complete description of the arboreal Galois representation of a certain postcritically finite cubic polynomial over a large class of number fields and for a large class of basepoints. This is the first such example that is not conjugate to a power map, Chebyshev polynomial, or Lattès map. The associated Galois action on an infinite ternary rooted tree has Hausdorff dimension bounded strictly between that of the infinite wreath product of cyclic groups and that of the infinite wreath… 
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