License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2023.75
URN: urn:nbn:de:0030-drops-186098
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18609/
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Paviet Salomon, Léo ; Vanier, Pascal

Realizing Finitely Presented Groups as Projective Fundamental Groups of SFTs

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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. 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.

BibTeX - Entry

@InProceedings{pavietsalomon_et_al:LIPIcs.MFCS.2023.75,
  author =	{Paviet Salomon, L\'{e}o and Vanier, Pascal},
  title =	{{Realizing Finitely Presented Groups as Projective Fundamental Groups of SFTs}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{75:1--75:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18609},
  URN =		{urn:nbn:de:0030-drops-186098},
  doi =		{10.4230/LIPIcs.MFCS.2023.75},
  annote =	{Keywords: Subshifts, Wang tiles, Dynamical Systems, Computability, Subshift of Finite Type, Fundamental Group}
}

Keywords: Subshifts, Wang tiles, Dynamical Systems, Computability, Subshift of Finite Type, Fundamental Group
Collection: 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)
Issue Date: 2023
Date of publication: 21.08.2023

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