The Dehn functions of $Out(F_n)$ and $Aut(F_n)$

Bridson, Martin R.; Vogtmann, Karen

The Dehn functions of

O u t (F_{n})

and

A u t (F_{n})

[Les fonctions de Dehn de

O u t (F_{n})

A u t (F_{n})

]

Bridson, Martin R. ; Vogtmann, Karen

Annales de l'Institut Fourier, Tome 62 (2012), p. 1811-1817 / Harvested from Numdam

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Résumé
Abstract

Pour $n$ au moins 3, les fonctions de Dehn de $O u t (F_{n})$ et $A u t (F_{n})$ sont exponentielles. Hatcher et Vogtmann ont montré qu’elles étaient au plus exponentielles, et la borne inférieure a été établie par Bridson et Vogtmann dans le cas $n = 3$ . Handel et Mosher ont complété la démonstration en ramenant la preuve de la borne inférieure pour $n$ au moins 4 au cas $n = 3$ . Dans cet article, nous donnons un argument plus direct permettant de passer du cas $n = 3$ au cas général.

For $n$ at least 3, the Dehn functions of $O u t (F_{n})$ and $A u t (F_{n})$ are exponential. Hatcher and Vogtmann proved that they are at most exponential, and the complementary lower bound in the case $n = 3$ was established by Bridson and Vogtmann. Handel and Mosher completed the proof by reducing the lower bound for $n$ bigger than 3 to the case $n = 3$ . In this note we give a shorter, more direct proof of this last reduction.

Publié le : 2012-01-01

MR 3025154 | Zbl 1259.20048

DOI : https://doi.org/10.5802/aif.2736
Classification: 20F65, 20F28, 53C24, 57S25
Mots clés: groupes des automorphismes des groupes libres, Fonctions de Dehn

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     author = {Bridson, Martin R. and Vogtmann, Karen},
     title = {The Dehn functions of $Out(F\_n)$ and $Aut(F\_n)$},
     journal = {Annales de l'Institut Fourier},
     volume = {62},
     year = {2012},
     pages = {1811-1817},
     doi = {10.5802/aif.2736},
     zbl = {1259.20048},
     mrnumber = {3025154},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2012__62_5_1811_0}
}

Bridson, Martin R.; Vogtmann, Karen. The Dehn functions of $Out(F_n)$ and $Aut(F_n)$. Annales de l'Institut Fourier, Tome 62 (2012) pp. 1811-1817. doi : 10.5802/aif.2736. http://gdmltest.u-ga.fr/item/AIF_2012__62_5_1811_0/

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