We prove that every injective simplicial map between flip graphs is induced by a subsurface inclusion , 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.
Keywords: Triangulation graph, flip, embedding
Mot clés : Graphe des triangulations, flip, plongement
@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}, pages = {2037--2055}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {65}, number = {5}, year = {2015}, doi = {10.5802/aif.2981}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2981/} }
TY - JOUR AU - Aramayona, Javier AU - Koberda, Thomas AU - Parlier, Hugo TI - Injective maps between flip graphs JO - Annales de l'Institut Fourier PY - 2015 SP - 2037 EP - 2055 VL - 65 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2981/ DO - 10.5802/aif.2981 LA - en ID - AIF_2015__65_5_2037_0 ER -
%0 Journal Article %A Aramayona, Javier %A Koberda, Thomas %A Parlier, Hugo %T Injective maps between flip graphs %J Annales de l'Institut Fourier %D 2015 %P 2037-2055 %V 65 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2981/ %R 10.5802/aif.2981 %G en %F 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://archive.numdam.org/articles/10.5802/aif.2981/
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