Approximate roots of pseudo-Anosov diffeomorphisms

Gendron, T. M.

Approximate roots of pseudo-Anosov diffeomorphisms
[Racines approximatives des difféormophismes pseudo-Anosov]

Gendron, T. M.

Annales de l'Institut Fourier, Tome 59 (2009), p. 1413-1442 / Harvested from Numdam

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Résumé
Abstract

La Conjecture de la Racine prévoit que chaque difféomorphisme pseudo-Anosov d’une surface fermée a une racine $n$ ième approximative de Teichmüller pour tout $n \geq 2$ . Dans cet article, on remplace la topologie de Teichmüller par la topologie hauteur-longueur – celle qui est induite par la convergence des différentielles quadratiques tangentes relativement aux fonctionnelles hauteurs et longueurs simultanément – et on prouve que chaque difféomorphisme pseudo-Anosov d’une surface fermée a une racine $n$ ième approximative hauteur-longueur pour tout $n \geq 2$ .

The Root Conjecture predicts that every pseudo-Anosov diffeomorphism of a closed surface has Teichmüller approximate $n$ th roots for all $n \geq 2$ . In this paper, we replace the Teichmüller topology by the heights-widths topology – that is induced by convergence of tangent quadratic differentials with respect to both the heights and widths functionals – and show that every pseudo-Anosov diffeomorphism of a closed surface has heights-widths approximate $n$ th roots for all $n \geq 2$ .

Publié le : 2009-01-01

MR 2566966 | Zbl 1179.30044

DOI : https://doi.org/10.5802/aif.2469
Classification: 30F60, 32G15
Mots clés: espace de Teichmüller, difféomorphisme pseudo-Anosov, conjecture de la racine

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     title = {Approximate roots of pseudo-Anosov diffeomorphisms},
     journal = {Annales de l'Institut Fourier},
     volume = {59},
     year = {2009},
     pages = {1413-1442},
     doi = {10.5802/aif.2469},
     zbl = {1179.30044},
     mrnumber = {2566966},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2009__59_4_1413_0}
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Gendron, T. M. Approximate roots of pseudo-Anosov diffeomorphisms. Annales de l'Institut Fourier, Tome 59 (2009) pp. 1413-1442. doi : 10.5802/aif.2469. http://gdmltest.u-ga.fr/item/AIF_2009__59_4_1413_0/

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