An approximation of the spectral gap for the Laplace operator on SAut(𝔽₅)

This is the dataset accompanying Aut(𝔽₅) has property (T) 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/ oSAutF5_r2/delta.jld oSAutF5_r2/orbits.jld oSAutF5_r2/preps.jld oSAutF5_r2/U_pis.jld oSAutF5_r2/pm.jld oSAutF5_r2/1.2/ oSAutF5_r2/1.2/full_2017-11-27T20:02:27.253.log oSAutF5_r2/1.2/SDPmatrix.jld oSAutF5_r2/1.2/solver_2017-11-27T20:05:39.134.log oSAutF5_r2/1.2/lambda.jld To replicate computation of the spectral gap clone GroupsWithPropertyT repository and checkout the 1712.07167 branch: git clone https://git.wmi.amu.edu.pl/kalmar/GroupsWithPropertyT.git cd ./GroupsWithPropertyT git checkout 1712.07167 Then unpack the content of oSAutF5_r2.tar.xz in GroupsWithPropertyT folder. You need julia-0.6. In julias REPL run Pkg.add("ArgParse") Pkg.add("Nemo") Pkg.clone("https://git.wmi.amu.edu.pl/kalmar/Groups.jl.git") Pkg.checkout("Groups", "1712.07167") Pkg.clone("https://git.wmi.amu.edu.pl/kalmar/GroupRings.jl.git") Pkg.checkout("GroupRings", "1712.07167") Pkg.clone("https://git.wmi.amu.edu.pl/kalmar/PropertyT.jl.git") Pkg.checkout("PropertyT", "1712.07167") Pkg.checkout("SCS") Pkg.build("SCS") Finally, to verify that the Laplace operator on SAut(𝔽₅) (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 *.jld files from the oSAutF5_r2 folder (but the ones in 1.2 folder) and run the same command again. Note: You need at least 32GB of RAM and spare 24h of Your CPU. This research was supported in part by PL-Grid Infrastructure.