# 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

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topGendron, 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 -

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