Injective maps between flip graphs
Annales de l'Institut Fourier, Volume 65 (2015) no. 5, p. 2037-2055

We prove that every injective simplicial map (S)(S ' ) between flip graphs is induced by a subsurface inclusion SS ' , except in finitely many cases. This extends a result of Korkmaz–Papadopoulos which asserts that every automorphism of the flip graph of a surface without boundary is induced by a surface homeomorphism.

Nous montrons que, sauf dans quelques cas exceptionnels, toute application injective entre graphes de triangulations d’une surface est induite par une inclusion. Cela généralise un résultat de Korkmaz et Papadopoulos qui dit que tout automorphisme du graphe de triangulations d’une surface sans bord est induit par un homéomorphisme de la surface.

DOI : https://doi.org/10.5802/aif.2981
Classification:  57M50,  05C10,  05C60
Keywords: Triangulation graph, flip, embedding
@article{AIF_2015__65_5_2037_0,
     author = {Aramayona, Javier and Koberda, Thomas and Parlier, Hugo},
     title = {Injective maps between flip graphs},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {65},
     number = {5},
     year = {2015},
     pages = {2037-2055},
     doi = {10.5802/aif.2981},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2015__65_5_2037_0}
}
Aramayona, Javier; Koberda, Thomas; Parlier, Hugo. Injective maps between flip graphs. Annales de l'Institut Fourier, Volume 65 (2015) no. 5, pp. 2037-2055. doi : 10.5802/aif.2981. http://www.numdam.org/item/AIF_2015__65_5_2037_0/

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