Realizing finitely presented groups as projective fundamental groups of SFTs

Léo Paviet Salomon (1) , Pascal Vanier (1)

1 Equipe AMACC - Laboratoire GREYC - UMR6072

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 and we show that any finitely presented group can be realized as a projective fundamental group of some SFT.

Keywords: Subshifts; Wang tiles; Dynamical Systems; Computability; Subshift of Finite Type; Fundamental Group

Domains: Discrete Mathematics [cs.DM]

Léo Paviet Salomon, Pascal Vanier. Realizing finitely presented groups as projective fundamental groups of SFTs. 2022. ⟨hal-03622497v1⟩