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

2016/11/18 by Anh Tuan Bui, Bui, Anh Tuan, Alexander D. Rahm +3 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1611.06099

openalex publication_date 2016/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

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

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