Arkiv för Matematik
- Ark. Mat.
- Volume 54, Number 2 (2016), 243-275.
A geometric interpretation of the Schützenberger group of a minimal subshift
Jorge Almeida and Alfredo Costa
Full-text: Open access
Abstract
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.
Note
Work partially supported respectively by CMUP (UID/MAT/00144/2013) and CMUC (UID/MAT/00324/2013), which are funded by FCT (Portugal) with national (MCTES) and European structural funds through the programs FEDER, under the partnership agreement PT2020.
Article information
Source
Ark. Mat., Volume 54, Number 2 (2016), 243-275.
Dates
Received: 24 July 2015
Revised: 23 December 2015
First available in Project Euclid: 30 January 2017
Permanent link to this document
https://projecteuclid.org/euclid.afm/1485802749
Digital Object Identifier
doi:10.1007/s11512-016-0233-7
Mathematical Reviews number (MathSciNet)
MR3546353
Zentralblatt MATH identifier
06696586
Rights
2016 © Institut Mittag-Leffler
Citation
Almeida, Jorge; Costa, Alfredo. A geometric interpretation of the Schützenberger group of a minimal subshift. Ark. Mat. 54 (2016), no. 2, 243--275. doi:10.1007/s11512-016-0233-7. https://projecteuclid.org/euclid.afm/1485802749
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