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Annals of Mathematics
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arXiv.org e-Print Archive
Preprint . 2009
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Annals of Mathematics
Article . 2013 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2009
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Annals of Mathematics
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The Dehn function of SL(n;Z)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 May 2013Embargo end date: 01 Jan 2009 English Publisher:Annals of MathematicsJournal:Annals of Mathematics, volume 177, pages 969-1,027 (issn: 0003-486X, Copyright policy )
Authors: Robert Young;

doi: 10.4007/annals.2013.177.3.4 , 10.48550/arxiv.0912.2697

arXiv: http://arxiv.org/abs/0912.2697

The Dehn function of SL(n;Z)

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.

49 pages, 9 figures, revised version, to appear in Annals of Mathematics

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Keywords

Mathematics - Geometric Topology, 20F65, 22E40, FOS: Mathematics, Geometric Topology (math.GT), Group Theory (math.GR), Mathematics - Group Theory

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
16
Average
Top 10%
Top 10%
Green
bronze
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