The Dehn function of SL(n;Z)

Details The Dehn function of SL(n;Z) The Dehn function of SL(n;Z)

2009-12-14

arxiv.org/abs/0912.2697v1

Mathematics

Group Theory

46 pages, 8 figures

Scientific paper

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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