The Farrell--Tate and Bredon homology for PSL_4(Z) via cell subdivisions

Anh Tuan Bui (1) , Alexander D. Rahm (2) , Matthias Wendt (3)

1 HCMUS - Ho Chi Minh City University of Science
2 NUIG - Department of Mathematics
3 Fakultät für Mathematik der Universität Duisburg-Essen

We provide some new computations of Farrell–Tate and Bredon (co)homology for arithmetic groups. For calculations of Farrell–Tate or Bredon homology, one needs cell complexes wherecell stabilizers fix their cells pointwise. We provide two algorithms computing an efficient subdivision of a complex to achieve this rigidity property. Applying these algorithms to available cell complexes for PSL4(Z) provides computations of Farrell–Tate cohomology for small primes as well as the Bredon homology for the classifying spaces of proper actions with coefficients in the complex representation ring.

Domaines: K-théorie et homologie [math.KT]

Anh Tuan Bui, Alexander D. Rahm, Matthias Wendt. The Farrell--Tate and Bredon homology for PSL_4(Z) via cell subdivisions. Journal of Pure and Applied Algebra, 2019, 223 (7), pp.2872-2888. ⟨10.1016/j.jpaa.2018.10.002⟩. ⟨hal-01398162v4⟩