Approximate roots of pseudo-Anosov diffeomorphisms
Annales de l'Institut Fourier, Volume 59 (2009) no. 4, p. 1413-1442

The Root Conjecture predicts that every pseudo-Anosov diffeomorphism of a closed surface has Teichmüller approximate nth roots for all n2. 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 nth roots for all n2.

La Conjecture de la Racine prévoit que chaque difféomorphisme pseudo-Anosov d’une surface fermée a une racine nième approximative de Teichmüller pour tout n2. 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 nième approximative hauteur-longueur pour tout n2.

DOI : https://doi.org/10.5802/aif.2469
Classification:  30F60,  32G15
Keywords: Teichmuller space, pseudo-Anosov diffeomorphism, root conjecture
@article{AIF_2009__59_4_1413_0,
     author = {Gendron, T. M.},
     title = {Approximate roots of pseudo-Anosov diffeomorphisms},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {59},
     number = {4},
     year = {2009},
     pages = {1413-1442},
     doi = {10.5802/aif.2469},
     mrnumber = {2566966},
     zbl = {1179.30044},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2009__59_4_1413_0}
}
Gendron, T. M. Approximate roots of pseudo-Anosov diffeomorphisms. Annales de l'Institut Fourier, Volume 59 (2009) no. 4, pp. 1413-1442. doi : 10.5802/aif.2469. http://www.numdam.org/item/AIF_2009__59_4_1413_0/

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