On a Nielsen–Thurston classification theory for cluster modular groups
[Sur une théorie de classification Nielsen–Thurston pour les groupes modulaires de cluster]
Annales de l'Institut Fourier, Tome 69 (2019) no. 2, pp. 515-560.

Nous classons les éléments d’un groupe modulaire de cluster en trois types. Nous les caractérisons en termes de propriété de point fixe de l’action sur les compactifications tropicales associées à l’ensemble de cluster correspondant. La caractérisation donne un analogue de la théorie de classification de Nielsen–Thurston sur le groupe modulaire d’une surface.

We classify elements of a cluster modular group into three types. We characterize them in terms of fixed point property of the action on the tropical compactifications associated with the corresponding cluster ensemble. The characterization gives an analogue of the Nielsen–Thurston classification theory on the mapping class group of a surface.

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DOI : https://doi.org/10.5802/aif.3250
Classification : 13F60,  30F60,  57M50
Mots clés : groupes modulaires de cluster, groupes modulaire, théorie de Teichmuller décorée
@article{AIF_2019__69_2_515_0,
     author = {Ishibashi, Tsukasa},
     title = {On a Nielsen{\textendash}Thurston classification theory for cluster modular groups},
     journal = {Annales de l'Institut Fourier},
     pages = {515--560},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {69},
     number = {2},
     year = {2019},
     doi = {10.5802/aif.3250},
     zbl = {07067411},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.3250/}
}
Ishibashi, Tsukasa. On a Nielsen–Thurston classification theory for cluster modular groups. Annales de l'Institut Fourier, Tome 69 (2019) no. 2, pp. 515-560. doi : 10.5802/aif.3250. http://archive.numdam.org/articles/10.5802/aif.3250/

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