# The Dehn functions of $Out\left({F}_{n}\right)$ and $Aut\left({F}_{n}\right)$

Martin R. Bridson^{[1]}; Karen Vogtmann^{[2]}

- [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 (2012)

- Volume: 62, Issue: 5, page 1811-1817
- ISSN: 0373-0956

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topBridson, Martin R., and Vogtmann, Karen. "The Dehn functions of $Out(F_n)$ and $Aut(F_n)$." Annales de l’institut Fourier 62.5 (2012): 1811-1817. <http://eudml.org/doc/251062>.

@article{Bridson2012,

abstract = {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.},

affiliation = {Mathematical Institute 24-29 St Giles’ Oxford OX1 3LB (U.K.); Cornell University Department of Mathematics Ithaca NY 14853 (USA)},

author = {Bridson, Martin R., Vogtmann, Karen},

journal = {Annales de l’institut Fourier},

keywords = {Automorphism groups of free groups; Dehn functions; automorphism groups of free groups; outer automorphisms},

language = {eng},

number = {5},

pages = {1811-1817},

publisher = {Association des Annales de l’institut Fourier},

title = {The Dehn functions of $Out(F_n)$ and $Aut(F_n)$},

url = {http://eudml.org/doc/251062},

volume = {62},

year = {2012},

}

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

PB - Association des Annales de l’institut Fourier

VL - 62

IS - 5

SP - 1811

EP - 1817

AB - 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.

LA - eng

KW - Automorphism groups of free groups; Dehn functions; automorphism groups of free groups; outer automorphisms

UR - http://eudml.org/doc/251062

ER -

## References

top- Emina Alibegovic, Translation lengths in $\mathrm{Out}\left({F}_{n}\right)$, Geom. Dedicata 92 (2002), 87-93 Zbl1041.20024MR1934012
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- M. R. Bridson, Karen Vogtmann, On the geometry of the automorphism group of a free group, Bull. Math Londres. Soc. 27 (1995), 544-552 Zbl0836.20045MR1348708
- M. R. Bridson, Karen Vogtmann, Automorphism groups of free groups, surface groups and free abelian groups, Problems on mapping class groups and related topics 74 (2006), 301-316, Amer. Math. Soc., Providence, RI Zbl1184.20034MR2264548
- Marc Culler, Karen Vogtmann, Moduli of graphs and automorphisms of free groups, Invent. Math. 84 (1986), 91-119 Zbl0589.20022MR830040
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- Michael Handel, Lee Mosher, Lipschitz retraction and distortion for subgroups of $\mathrm{Out}\left({F}_{n}\right)$, arXiv:1009.5018 (2010) Zbl1285.20033
- Allen Hatcher, Karen Vogtmann, Isoperimetric inequalities for automorphism groups of free groups, Pacific J. Math. 173 (1996), 425-441 Zbl0862.20030MR1394399
- Lee Mosher, Mapping class groups are automatic, Ann. of Math. (2) 142 (1995), 303-384 Zbl0867.57004MR1343324
- Robert Young, The Dehn function of SL(n;$\mathbb{Z}$), (2009)

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