The Dehn function of SL(n;Z)
classification
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math.GT
keywords
dehnfunctiontrianglescombinatorialdecomposingdiscelementaryfill
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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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