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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 969-1027 |
| Number of pages | 59 |
| Journal | Annals of Mathematics |
| Volume | 177 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2013 |
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty