A geometric interpretation of the Schützenberger group of a minimal subshift

@article{Almeida2016AGI,
  title={A geometric interpretation of the Sch{\"u}tzenberger group of a minimal subshift},
  author={Jorge Almeida and A. Costa},
  journal={Arkiv f{\"o}r Matematik},
  year={2016},
  volume={54},
  pages={243-275}
}
The first author has associated in a natural way a profinite group to each irreducible subshift. The group in question was initially obtained as a maximal subgroup of a free profinite semigroup. In the case of minimal subshifts, the same group is shown in the present paper to also arise from geometric considerations involving the Rauzy graphs of the subshift. Indeed, the group is shown to be isomorphic to the inverse limit of the profinite completions of the fundamental groups of the Rauzy… 

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