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T. M. Gendron
Approximate roots of pseudo-Anosov diffeomorphisms
(Racines approximatives des difféormophismes pseudo-Anosov)
Annales de l'institut Fourier, 59 no. 4 (2009), p. 1413-1442, doi: 10.5802/aif.2469
Article PDF | Reviews MR 2566966 | Zbl 1179.30044
Class. Math.: 30F60, 32G15
Keywords: Teichmuller space, pseudo-Anosov diffeomorphism, root conjecture

Résumé - Abstract

The Root Conjecture predicts that every pseudo-Anosov diffeomorphism of a closed surface has Teichmüller approximate $n$th roots for all $n\ge 2$. 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 $n\ge 2$.

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