A geometric interpretation of the Schutzenberger group of a minimal subshift

• Type: Article in International Scientific Journal
• Date: 2016

Authors

Almeida, J (Author) FCUP; Costa, A (Author) Other

Journal

Title: Arkiv for Matematik

Vol. 54

Pages: 243-275

ISSN: 0004-2080

Publisher: International Press of Boston, Inc.

Indexing

ISI Web of Knowledge - 6 Citations

Scopus - 6 Citations

Other information

Authenticus ID: P-00K-DKX

DOI: 10.1007/s11512-016-0233-7

Abstract (EN): 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 Berth, et al.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 33