A polynomial isoperimetric inequality for SL(n,Z)

Details A polynomial isoperimetric inequality for SL(n,Z) A polynomial isoperimetric inequality for SL(n,Z)

2009-03-13

arxiv.org/abs/0903.2495v1

Mathematics

Group Theory

22 pages

Scientific paper

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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