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The Farrell--Tate and Bredon homology for PSL_4(Z) via cell subdivisions ; Rahm, Alexander ; in Journal of Pure and Applied Algebra (2019), 223(7), 2872-2888 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 where cell stabilizers fix ... [more ▼] 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 where cell 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 PSL_4(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. [less ▲] Detailed reference viewed: 156 (15 UL)Bounds for the mod 2 cohomology of GL_2(Z[sqrt(-2)][1/2]) ; Rahm, Alexander E-print/Working paper (2017) Detailed reference viewed: 30 (0 UL)Verification of the Quillen conjecture in the rank 2 imaginary quadratic case Rahm, Alexander ; E-print/Working paper (n.d.) We confirm a conjecture of Quillen in the case of the mod 2 cohomology of arithmetic groups SL_2(A[1/2]), where A is an imaginary quadratic ring of integers. To make explicit the free module structure on ... [more ▼] We confirm a conjecture of Quillen in the case of the mod 2 cohomology of arithmetic groups SL_2(A[1/2]), where A is an imaginary quadratic ring of integers. To make explicit the free module structure on the cohomology ring conjectured by Quillen, we compute the mod 2 cohomology of SL_2(Z[sqrt(−2)][1/2]) via the amalgamated decomposition of the latter group. [less ▲] Detailed reference viewed: 46 (1 UL) |
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