Approximate roots of pseudo-Anosov diffeomorphisms
[Racines approximatives des difféormophismes pseudo-Anosov]
Annales de l'Institut Fourier, Tome 59 (2009) no. 4, pp. 1413-1442.

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.

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.

DOI : 10.5802/aif.2469
Classification : 30F60, 32G15
Keywords: Teichmuller space, pseudo-Anosov diffeomorphism, root conjecture
Mot clés : espace de Teichmüller, difféomorphisme pseudo-Anosov, conjecture de la racine
Gendron, T. M. 1

1 Universidad Nacional Autonoma de México Instituto de Matemáticas Av. Universidad S/N Unidad Cuernavaca C.P. 62210 Cuernavaca Morelos (MÉXICO)
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Gendron, T. M. Approximate roots of pseudo-Anosov diffeomorphisms. Annales de l'Institut Fourier, Tome 59 (2009) no. 4, pp. 1413-1442. doi : 10.5802/aif.2469. http://www.numdam.org/articles/10.5802/aif.2469/

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