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arXiv · 1503.06504

Coassembly and the $K$-theory of finite groups

Cary Malkiewich
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Abstract

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.

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Cary Malkiewich. 2016-11-15. Coassembly and the $K$-theory of finite groups. https://doi.org/10.1016/j.aim.2016.11.017

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