The dehn function of sl(n; ℤ)

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)969-1027
Number of pages59
JournalAnnals of Mathematics
Volume177
Issue number3
DOIs
StatePublished - 2013

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Dehn Function
Triangle
Elementary matrix

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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The dehn function of sl(n; ℤ). / Young, Robert.

In: Annals of Mathematics, Vol. 177, No. 3, 2013, p. 969-1027.

Research output: Contribution to journalArticle

Young, Robert. / The dehn function of sl(n; ℤ). In: Annals of Mathematics. 2013 ; Vol. 177, No. 3. pp. 969-1027.
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