A polynomial isoperimetric inequality for SL(n,Z)
Group Theory
2009-03-17 v1
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.
Keywords
Cite
@article{arxiv.0903.2495,
title = {A polynomial isoperimetric inequality for SL(n,Z)},
author = {Robert Young},
journal= {arXiv preprint arXiv:0903.2495},
year = {2009}
}
Comments
22 pages