For at least 3, the Dehn functions of and are exponential. Hatcher and Vogtmann proved that they are at most exponential, and the complementary lower bound in the case was established by Bridson and Vogtmann. Handel and Mosher completed the proof by reducing the lower bound for bigger than 3 to the case . In this note we give a shorter, more direct proof of this last reduction.
Pour au moins 3, les fonctions de Dehn de et 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 . Handel et Mosher ont complété la démonstration en ramenant la preuve de la borne inférieure pour au moins 4 au cas . Dans cet article, nous donnons un argument plus direct permettant de passer du cas au cas général.
Keywords: Automorphism groups of free groups, Dehn functions
Mot clés : groupes des automorphismes des groupes libres, Fonctions de Dehn
@article{AIF_2012__62_5_1811_0, 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}, pages = {1811--1817}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {62}, number = {5}, year = {2012}, doi = {10.5802/aif.2736}, zbl = {1259.20048}, mrnumber = {3025154}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2736/} }
TY - JOUR AU - Bridson, Martin R. AU - Vogtmann, Karen TI - The Dehn functions of $Out(F_n)$ and $Aut(F_n)$ JO - Annales de l'Institut Fourier PY - 2012 SP - 1811 EP - 1817 VL - 62 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2736/ DO - 10.5802/aif.2736 LA - en ID - AIF_2012__62_5_1811_0 ER -
%0 Journal Article %A Bridson, Martin R. %A Vogtmann, Karen %T The Dehn functions of $Out(F_n)$ and $Aut(F_n)$ %J Annales de l'Institut Fourier %D 2012 %P 1811-1817 %V 62 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2736/ %R 10.5802/aif.2736 %G en %F 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, Volume 62 (2012) no. 5, pp. 1811-1817. doi : 10.5802/aif.2736. http://archive.numdam.org/articles/10.5802/aif.2736/
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