2015/03/31 by Cary Malkiewich
Chemistry · Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Algorithm #Chemistry #Cohomology #Computation #Equivariant cohomology #Equivariant map #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Mathematics #Norm (philosophy) #Physics #Pure mathematics #Quantum mechanics #Ring (chemistry) #Spectrum (functional analysis) #math.AT #math.KT #msc:18F25 #msc:19D10 #msc:55R12 #msc:55R70
paper · pdf · doi:10.1016/j.aim.2016.11.017
published as Advances in Mathematics 307C (2017) pp. 100-146 · Accepted version. 44 pages
arxiv created 2016/11/15 · openalex publication_date 2016/11/22 · arxiv updated 2016/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the K-theory and Swan theory of the group ring R[G], when G is a finite group and R is any ring or ring spectrum. In this setting, the well-known assembly map for K(R[G]) has a companion called the coassembly map. We prove that their composite is the equivariant norm of K(R). This gives a splitting of both assembly and coassembly after K(n)-localization, a new map between Whitehead torsion and Tate cohomology, and a partial computation of K-theory of representations in the category of spectra.