The Dehn function of SL(n;Z)
Group Theory
2012-08-24 v2 Geometric Topology
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.
Cite
@article{arxiv.0912.2697,
title = {The Dehn function of SL(n;Z)},
author = {Robert Young},
journal= {arXiv preprint arXiv:0912.2697},
year = {2012}
}
Comments
49 pages, 9 figures, revised version, to appear in Annals of Mathematics