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arXiv · 0903.2495

A polynomial isoperimetric inequality for SL(n,Z)

Robert Young
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Abstract

We prove that when n>=5, the Dehn function of SL(n,Z) is at most quartic. The proof involves decomposing a disc in SL(n,R)/SO(n) into a quadratic number of loops in generalized Siegel sets. By mapping these loops 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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Robert Young. 2009-03-13. A polynomial isoperimetric inequality for SL(n,Z). https://arxiv.org/abs/0903.2495

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