Robert Young
Published 2009-12-14, updated 2012-08-22Version 2
We prove that when n >= 5, the Dehn function of SL(n;Z) is quadratic. The proof involves decomposing a disc in SL(n;R)/SO(n) into triangles of varying sizes. By mapping these triangles into SL(n;Z) and replacing large elementary matrices by "shortcuts," we obtain words of a particular form, and we use combinatorial techniques to fill these loops.
Comments: 49 pages, 9 figures, revised version, to appear in Annals of Mathematics
The Dehn function for Palindromic Sub-Group of $Aut(F_n)$
The Dehn function of Stallings' group
Explicit polynomial bounds on Dehn functions of subgroups of hyperbolic groups
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