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The weak regular coherence is a coarse property of a finitely generated group$\Gamma$. It was introduced by G. Carlsson and this author to play the role ofa weakening of Waldhausen's regular coherence as part of computation of theintegral K-theoretic assembly map. A new class of metric spaces (sFDC) wasintroduced recently by A. Dranishnikov and M. Zarichnyi. This class includesmost notably the spaces with finite decomposition complexity (FDC) studied byE. Guentner, D. Ramras, R. Tessera, and G. Yu. The main theorem of this papershows that a group that has finite $K(\Gamma,1)$ and sFDC is weakly regularcoherent. As a consequence, the integral K-theoretic assembly maps areisomorphisms in all dimensions for any group that has finite $K(\Gamma,1)$ andFDC. In particular, the Whitehead group $Wh (\Gamma)$ is trivial for suchgroups.

Weak coherence of groups and finite decomposition complexity