Mapping class group dynamics on Aff()-characters.
[Dynamique du groupe modulaire sur les caractères affines]
Annales de l'Institut Fourier, Tome 66 (2016) no. 2, pp. 729-751.

Nous prouvons dans cet article qu’en genre plus grand que deux, l’action du groupe modulaire sur les caractères affines est ergodique. Un corollaire de ce résultat est que presque toute représentation du groupe fondamental de S dans le groupe affine complexe est l’holonomie d’une structure affine branchée sur S, où S est une surface fermée orientable de genre plus grand que deux.

We prove that in genus bigger than 2, the mapping class group action on Aff()-characters is ergodic. This implies that almost every representation π 1 SAff() is the holonomy of a branched affine structure on S, where S is a closed orientable surface of genus g2.

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DOI : https://doi.org/10.5802/aif.3024
Classification : 22D40,  20F39,  57M05
Mots clés : théorie ergodique, groupe modulaire, groupe de Torelli, variété de caractères, groupe affine complex, structure affine branchée
@article{AIF_2016__66_2_729_0,
     author = {Ghazouani, Selim},
     title = {Mapping class group dynamics on $\mathrm{Aff}(\mathbb{C})$-characters.},
     journal = {Annales de l'Institut Fourier},
     pages = {729--751},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {66},
     number = {2},
     year = {2016},
     doi = {10.5802/aif.3024},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.3024/}
}
Ghazouani, Selim. Mapping class group dynamics on $\mathrm{Aff}(\mathbb{C})$-characters.. Annales de l'Institut Fourier, Tome 66 (2016) no. 2, pp. 729-751. doi : 10.5802/aif.3024. http://archive.numdam.org/articles/10.5802/aif.3024/

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