Geodesic
The Dehn function of $\mathrm{SL}(n;\mathbb{Z})$
Robert Young1
1 Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, ON M5S 2E4, Canada
Annals of mathematics, Tome 177 (2013) no. 3, pp. 969-1027.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove that when $n\ge 5$, the Dehn function of $\mathrm{SL}(n;\mathbb{Z})$ is quadratic. The proof involves decomposing a disc in $\mathrm{SL}(n;\mathbb{R})/\mathrm{SO}(n)$ into triangles of varying sizes. By mapping these triangles into $\mathrm{SL}(n;\mathbb{Z})$ and replacing large elementary matrices by “shortcuts,” we obtain words of a particular form, and we use combinatorial techniques to fill these loops.
DOI : 10.4007/annals.2013.177.3.4

Robert Young 1

1 Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, ON M5S 2E4, Canada 
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Robert Young. The Dehn function of $\mathrm{SL}(n;\mathbb{Z})$. Annals of mathematics, Tome 177 (2013) no. 3, pp. 969-1027. doi : 10.4007/annals.2013.177.3.4. http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.177.3.4/

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