On the 𝐾-theory of crystallographic groups

Tsapogas, Georgios

doi:10.1090/S0002-9947-1995-1308025-1

On the $K$-theory of crystallographic groups
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by Georgios Tsapogas PDF

Trans. Amer. Math. Soc. 347 (1995), 2781-2794 Request permission

Abstract:

For any crystallographic group $\Gamma$ we show that the groups ${K_i}(\Gamma )$ are isomorphic, via the forget control map, to the controlled $K$-groups ${K_i}{(\Gamma )_c}$, for all $i \leqslant 1$ and for an appropriate choice of the control map. By using this result and under a mild hypothesis on the crystallographic group $\Gamma$, it is proved that ${K_i}(\Gamma ) = 0$ for all $i \leqslant - 2$ and ${N^j}{K_i}(\Gamma ) = 0$ for all $i \leqslant - 1$ and $j > 0$.

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