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DOI: 10.4230/LIPIcs.MFCS.2023.75

Realizing Finitely Presented Groups as Projective Fundamental Groups of SFTs

Authors: Léo Paviet Salomon and Pascal Vanier

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

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.

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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)

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@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/entities/document/10.4230/LIPIcs.MFCS.2023.75},
  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}
}

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Realizing Finitely Presented Groups as Projective Fundamental Groups of SFTs

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