An Approximation Of The Spectral Gap For The Laplace Operator On Saut(𝔽₅)

This is the dataset accompanying <em>Aut(𝔽₅) has property (T)</em> paper (https://arxiv.org/abs/1712.07167). See Section 4 thereof for a detailed description of the content of the included files: tar --list -f ./oSAutF5_r2.tar.xz oSAutF5_r2/<br> oSAutF5_r2/delta.jld<br> oSAutF5_r2/orbits.jld<br> oSAutF5_r2/preps.jld<br> oSAutF5_r2/U_pis.jld<br> oSAutF5_r2/pm.jld<br> oSAutF5_r2/1.2/<br> oSAutF5_r2/1.2/full_2017-11-27T20:02:27.253.log<br> oSAutF5_r2/1.2/SDPmatrix.jld<br> oSAutF5_r2/1.2/solver_2017-11-27T20:05:39.134.log<br> oSAutF5_r2/1.2/lambda.jld To replicate computation of the spectral gap clone <em>GroupsWithPropertyT</em> repository and checkout the <em>1712.07167</em> branch: git clone https://git.wmi.amu.edu.pl/kalmar/GroupsWithPropertyT.git<br> cd ./GroupsWithPropertyT<br> git checkout 1712.07167 Then unpack the content of <em>oSAutF5_r2.tar.xz</em> in <em>GroupsWithPropertyT</em> folder. You need <em>julia-0.6. </em>In <em>julia</em>s REPL run Pkg.add("ArgParse")<br> Pkg.add("Nemo")<br> Pkg.clone("https://git.wmi.amu.edu.pl/kalmar/Groups.jl.git")<br> Pkg.checkout("Groups", "1712.07167")<br> Pkg.clone("https://git.wmi.amu.edu.pl/kalmar/GroupRings.jl.git")<br> Pkg.checkout("GroupRings", "1712.07167")<br> Pkg.clone("https://git.wmi.amu.edu.pl/kalmar/PropertyT.jl.git")<br> Pkg.checkout("PropertyT", "1712.07167")<br> Pkg.checkout("SCS")<br> Pkg.build("SCS") Finally, to verify that the Laplace operator on <em>SAut(𝔽₅)</em> (associated to the standard generating set) has spectral gap of at least 1.2 run julia AutFN_orbit.jl -N 5 --upper-bound=1.2 If You want to generate the multiplication table and other files on Your own delete all <code>*.jld</code> files from the <code>oSAutF5_r2</code> folder (but the ones in <code>1.2</code> folder) and run the same command again. Note: You need at least <code>32</code>GB of RAM and spare <code>24</code>h of Your CPU. This research was supported in part by PL-Grid Infrastructure.