Injective maps between flip graphs

Aramayona, Javier; Koberda, Thomas; Parlier, Hugo

doi:10.5802/aif.2981

Injective maps between flip graphs
[Applications injectives entre graphes de triangulations]

Aramayona, Javier ¹ ; Koberda, Thomas ² ; Parlier, Hugo ³

¹ Université Paul Sabatier Institut de Mathématiques 118 Route de Narbonne 31000 Toulouse CEDEX 9 (France)
² Yale University Department of Mathematics PO Box 208283 New Haven, CT 06520-8283 (USA)
³ University of Fribourg Department of Mathematics CH-1700 Fribourg (Switzerland)

Annales de l'Institut Fourier, Tome 65 (2015) no. 5, pp. 2037-2055.

Résumé
Abstract

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.

We prove that every injective simplicial map $ℱ (S) \to ℱ (S^{'})$ between flip graphs is induced by a subsurface inclusion $S \to S^{'}$ , 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.

DOI : 10.5802/aif.2981

Classification : 57M50, 05C10, 05C60
Keywords: Triangulation graph, flip, embedding
Mot clés : Graphe des triangulations, flip, plongement

Affiliations des auteurs :

Aramayona, Javier ¹ ; Koberda, Thomas ² ; Parlier, Hugo ³

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Aramayona, Javier; Koberda, Thomas; Parlier, Hugo. Injective maps between flip graphs. Annales de l'Institut Fourier, Tome 65 (2015) no. 5, pp. 2037-2055. doi : 10.5802/aif.2981. http://www.numdam.org/articles/10.5802/aif.2981/

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