10.5281/zenodo.1133441
https://zenodo.org/records/1133441
oai:zenodo.org:1133441
Kaluba, Marek
Marek
Kaluba
0000-0002-8777-8223
Adam Mickiewicz University, Poznań, Poland
Nowak, Piotr W.
Piotr W.
Nowak
0000-0002-6519-004X
Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland
Ozawa, Narutaka
Narutaka
Ozawa
Research Institute for Mathematical Sciences, Kyoto, Japan
An approximation of the spectral gap for the Laplace operator on SAut(𝔽₅)
Zenodo
2017
spectral gap
Laplace operator
SAut(F5)
property (T)
semidefinite optimization
2017-12-19
arXiv:1712.07167
10.5281/zenodo.1133440
https://zenodo.org/communities/eu
1.2
Creative Commons Attribution Share Alike 4.0 International
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.
European Commission
10.13039/501100000780
677120
Rigidity of groups and higher index theory