Pré-Publication, Document De Travail Année : 2025

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

Résumé

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).

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Dates et versions

hal-05168476 , version 1 (18-07-2025)
hal-05168476 , version 2 (10-03-2026)

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Anh Tuan Bui, Alexander D. Rahm, Matthias Wendt. The 2-torsion in the Farrell--Tate cohomology of PSL(4,Z), and torsion subcomplex reduction via discrete Morse theory. 2025. ⟨hal-05168476v1⟩
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