The Dehn function of SL(n, Z)

• 成果类型: Article
• 署名作者: Young, Robert
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2013.177.3.4
• 发表日期: 2013
• 页码: 969-1027
• 关键词: arithmetic groups; compactifications; conjecture; SUBGROUPS; geometry; lattices; PROOF

摘要

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.