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Approximate roots of pseudo-Anosov diffeomorphisms

T. M. Gendron (2009)

Annales de l’institut Fourier

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

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