Canonicality of Makanin–Razborov Diagrams – Counterexample
[Canonicalité des diagrammes de Makanin–Razborov – Contre-exemple]
Annales de l'Institut Fourier, Tome 70 (2020) no. 5, pp. 2027-2047.

Des ensembles de solutions à des systèmes d’équations à nombre fini de variables dans un groupe libre, sont équivalents à des ensembles d’homomorphismes d’un groupe de type fini fixé en un groupe libre. Chacun de ces ensembles peut être codé dans un diagramme, qui est connu pour être canonique pour un groupe de type fini fixé avec une partie génératrice fixée. Dans cet article, nous montrons que la construction dépend de la partie génératrice choisie pour le groupe de type fini donné.

Sets of solutions to systems of equations with finitely many variables in a free group, are equivalent to sets of homomorphisms from a fixed finitely generated group into a free group. The latter can be encoded in a diagram, which is known to be canonical for a fixed finitely generated group with a fixed generating set. In this paper we prove that the construction depends on the chosen generating set of the given finitely generated group.

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DOI : https://doi.org/10.5802/aif.3368
Classification : 20F65,  03C60
Mots clés : diagramme de Makanin–Razborov, partie génératrice, groupe limite, decomposition JSJ, mot Ivanov, automorphisme modulaire, théorie des modèles des groupes
@article{AIF_2020__70_5_2027_0,
     author = {Berk, Gili},
     title = {Canonicality of Makanin{\textendash}Razborov Diagrams {\textendash} Counterexample},
     journal = {Annales de l'Institut Fourier},
     pages = {2027--2047},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {70},
     number = {5},
     year = {2020},
     doi = {10.5802/aif.3368},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3368/}
}
Berk, Gili. Canonicality of Makanin–Razborov Diagrams – Counterexample. Annales de l'Institut Fourier, Tome 70 (2020) no. 5, pp. 2027-2047. doi : 10.5802/aif.3368. https://aif.centre-mersenne.org/articles/10.5802/aif.3368/

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