Abstract
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.

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