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)|
|Number of pages||59|
|Journal||Annals of Mathematics|
|State||Published - 2013|
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty