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Realizing finitely presented groups as projective fundamental groups of SFTs

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Bibliographic Details
Title:	Realizing finitely presented groups as projective fundamental groups of SFTs
Authors:	Paviet Salomon, Léo, Vanier, Pascal
Contributors:	Paviet Salomon, Léo, Léo Paviet Salomon and Pascal Vanier
Publisher Information:	Array, 2023.
Publication Year:	2023
Subject Terms:	Wang tiles, Computability, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Theory of computation → Models of computation, Subshift of Finite Type, Mathematics of computing → Discrete mathematics, ddc:004, Fundamental Group, Dynamical Systems, Subshifts
Description:	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.
Document Type:	Conference object Article
File Description:	application/pdf
Language:	English
DOI:	10.4230/lipics.mfcs.2023.75
Access URL:	https://hal.science/hal-03622497v2/document https://hal.science/hal-03622497v2 https://doi.org/10.4230/lipics.mfcs.2023.75 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.75
Rights:	CC BY
Accession Number:	edsair.dedup.wf.002..ffaf38a75fb4641bf1a6fa00b808fa01
Database:	OpenAIRE

Description
Abstract:	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.
DOI:	10.4230/lipics.mfcs.2023.75