The Dehn functions of Out(F n ) and Aut(F n )
Annales de l'Institut Fourier, Volume 62 (2012) no. 5, p. 1811-1817

For n at least 3, the Dehn functions of Out(F n ) and Aut(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.

Pour n au moins 3, les fonctions de Dehn de Out(F n ) et Aut(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.

DOI : https://doi.org/10.5802/aif.2736
Classification:  20F65,  20F28,  53C24,  57S25
Keywords: Automorphism groups of free groups, Dehn functions
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {62},
     number = {5},
     year = {2012},
     pages = {1811-1817},
     doi = {10.5802/aif.2736},
     mrnumber = {3025154},
     zbl = {1259.20048},
     language = {en},
     url = {http://www.numdam.org/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, Volume 62 (2012) no. 5, pp. 1811-1817. doi : 10.5802/aif.2736. http://www.numdam.org/item/AIF_2012__62_5_1811_0/

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