### 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) |
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Pages (from-to) | 969-1027 |

Number of pages | 59 |

Journal | Annals of Mathematics |

Volume | 177 |

Issue number | 3 |

DOIs | |

State | Published - 2013 |

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### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Annals of Mathematics*,

*177*(3), 969-1027. https://doi.org/10.4007/annals.2013.177.3.4

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

Research output: Contribution to journal › Article

*Annals of Mathematics*, vol. 177, no. 3, pp. 969-1027. https://doi.org/10.4007/annals.2013.177.3.4

}

TY - JOUR

T1 - The dehn function of sl(n; ℤ)

AU - Young, Robert

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84879325513&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84879325513&partnerID=8YFLogxK

U2 - 10.4007/annals.2013.177.3.4

DO - 10.4007/annals.2013.177.3.4

M3 - Article

VL - 177

SP - 969

EP - 1027

JO - Annals of Mathematics

JF - Annals of Mathematics

SN - 0003-486X

IS - 3

ER -