The 2-torsion in the Farrell--Tate cohomology of PSL(4,Z), and torsion subcomplex reduction via discrete Morse theory

In the present paper, we use discrete Morse theory to provide a new implementation of torsion subcomplex reduction for arithmetic groups. This leads both to a simpler algorithm as well as runtime improvements. To demonstrate the technique, we compute the mod 2 Farrell-Tate cohomology of PSL(4,Z).