Realizing Finitely Presented Groups as Projective Fundamental Groups of SFTs

Authors Léo Paviet Salomon, Pascal Vanier

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Author Details

Léo Paviet Salomon
  • Normandie Univ, UNICAEN, ENSICAEN, CNRS, GREYC, 14000 Caen, France
Pascal Vanier
  • Normandie Univ, UNICAEN, ENSICAEN, CNRS, GREYC, 14000 Caen, France


The authors would like to thank all the anonymous referees of this paper for their remarks which helped improve the exposition.

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Léo Paviet Salomon and Pascal Vanier. Realizing Finitely Presented Groups as Projective Fundamental Groups of SFTs. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 75:1-75:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Subshifts are sets of colourings - or tilings - of the plane, defined by local constraints. Historically introduced as discretizations of continuous dynamical systems, they are also heavily related to computability theory. In this article, we study a conjugacy invariant for subshifts, known as the projective fundamental group. It is defined via paths inside and between configurations. We show that any finitely presented group can be realized as a projective fundamental group of some SFT.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • Mathematics of computing → Discrete mathematics
  • Subshifts
  • Wang tiles
  • Dynamical Systems
  • Computability
  • Subshift of Finite Type
  • Fundamental Group


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