no. 5
The Dehn functions of Out(F n ) and Aut(F n )
[Les fonctions de Dehn de Out(F n ) et Aut(F n )]
Bridson, Martin R.1 ; Vogtmann, Karen2
1 Mathematical Institute 24-29 St Giles’ Oxford OX1 3LB (U.K.)
2 Cornell University Department of Mathematics Ithaca NY 14853 (USA)
Annales de l'Institut Fourier, Tome 62 (2012) no. 5, pp. 1811-1817.

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.

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.

DOI : 10.5802/aif.2736
Classification : 20F65, 20F28, 53C24, 57S25
Keywords: Automorphism groups of free groups, Dehn functions
Mot clés : groupes des automorphismes des groupes libres, Fonctions de Dehn

Bridson, Martin R. 1 ; Vogtmann, Karen 2

1 Mathematical Institute 24-29 St Giles’ Oxford OX1 3LB (U.K.)
2 Cornell University Department of Mathematics Ithaca NY 14853 (USA) 
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Bridson, Martin R.; Vogtmann, Karen. The Dehn functions of $Out(F_n)$ and $Aut(F_n)$. Annales de l'Institut Fourier, Tome 62 (2012) no. 5, pp. 1811-1817. doi : 10.5802/aif.2736. https://aif.centre-mersenne.org/articles/10.5802/aif.2736/

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