The dehn function of sl(n; ℤ)

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)969-1027
Number of pages59
JournalAnnals of Mathematics
Issue number3
StatePublished - 2013

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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