\(\mathbf {Aut(F}_2\mathbf )\) puzzles

  • Sylvain Barré
  • Mikael Pichot
Original Paper


This paper defines a tiling problem related to the automorphism group of \(F_2\). Our main result is that the corresponding tilings admit a complete, concrete classification.


Tilings Automorphisms of free groups Flat closing conjecture 

Mathematics Subject Classification

52C20 20F67 



We thank the referee for his numerous comments on this paper. The second author is partially supported by NSERC and a JSPS Grant held at the Research Institute for Mathematical Sciences in Kyoto.


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.McGill University Department of Mathematics and StatisticsMontrealCanada
  2. 2.Université Européenne de BretagneVannesFrance

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