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A geometric interpretation of the Schützenberger group of a minimal subshift

Jorge Almeida CMUP, Departamento de Matemática, Faculdade de Ciências, Universidade do Porto Alfredo Costa CMUC, Department of Mathematics, University of Coimbra

Geometric Analysis and Geometric Topology Group Theory and Lie Theory mathscidoc:1701.01011

Arkiv for Matematik, 1-33, 2015.7
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 graphs of the subshift. A further result involving geometric arguments on Rauzy graphs is a criterion for freeness of the profinite group of a minimal subshift based on the Return Theorem of Berthé et al.
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@inproceedings{jorge2015a,
  title={A geometric interpretation of the Schützenberger group of a minimal subshift},
  author={Jorge Almeida, and Alfredo Costa},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203407565615822},
  booktitle={Arkiv for Matematik},
  pages={1-33},
  year={2015},
}
Jorge Almeida, and Alfredo Costa. A geometric interpretation of the Schützenberger group of a minimal subshift. 2015. In Arkiv for Matematik. pp.1-33. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203407565615822.
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