Approximate roots of pseudo-Anosov diffeomorphisms

T. M. Gendron[1]

  • [1] Universidad Nacional Autonoma de México Instituto de Matemáticas Av. Universidad S/N Unidad Cuernavaca C.P. 62210 Cuernavaca Morelos (MÉXICO)

Annales de l’institut Fourier (2009)

  • Volume: 59, Issue: 4, page 1413-1442
  • ISSN: 0373-0956

Abstract

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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 .

How to cite

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Gendron, T. M.. "Approximate roots of pseudo-Anosov diffeomorphisms." Annales de l’institut Fourier 59.4 (2009): 1413-1442. <http://eudml.org/doc/10433>.

@article{Gendron2009,
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 $n\ge 2$.},
affiliation = {Universidad Nacional Autonoma de México Instituto de Matemáticas Av. Universidad S/N Unidad Cuernavaca C.P. 62210 Cuernavaca Morelos (MÉXICO)},
author = {Gendron, T. M.},
journal = {Annales de l’institut Fourier},
keywords = {Teichmuller space; pseudo-Anosov diffeomorphism; root conjecture; Teichmüller space; heights-widths topology; heights-widths roots},
language = {eng},
number = {4},
pages = {1413-1442},
publisher = {Association des Annales de l’institut Fourier},
title = {Approximate roots of pseudo-Anosov diffeomorphisms},
url = {http://eudml.org/doc/10433},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Gendron, T. M.
TI - Approximate roots of pseudo-Anosov diffeomorphisms
JO - Annales de l’institut Fourier
PY - 2009
PB - Association des Annales de l’institut Fourier
VL - 59
IS - 4
SP - 1413
EP - 1442
AB - 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 $n\ge 2$.
LA - eng
KW - Teichmuller space; pseudo-Anosov diffeomorphism; root conjecture; Teichmüller space; heights-widths topology; heights-widths roots
UR - http://eudml.org/doc/10433
ER -

References

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