2009/03/13 by Robert Young, Young, Robert
Mathematics · #20F65 #22E40 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20F65 #msc:22E40
paper · pdf · doi:10.48550/arxiv.0903.2495
22 pages
arxiv created 2009/03/13 · arxiv updated 2009/12/01
We prove that when n>=5, the Dehn function of SL(n,Z) is at most quartic. The proof involves decomposing a disc in SL(n,R)/SO(n) into a quadratic number of loops in generalized Siegel sets. By mapping these loops 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.