Using the isomorphism conjectures of Baum & Connes and Farrel & Jones, we compute the algebraic K-and L-theory and the topological K-theory of cocompact planar groups (= cocompact N.E.C-groups) and of groups G appearing in an extension 1 → Z n → G → π → 1 where π is a finite group and the conjugation π-action on Z n is free outside 0 ∈ Z n . These computations apply for instance to two-dimensional crystallographic groups and cocompact Fuchsian groups.
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