It is in some sense folklore that given two arbitrary abelian groups $G,H$ one can find a $C^\*$ algebra $A$ such that $K\_0(A)=G$ and $K\_1(A)=H$. My question is the following: what is known in the case of commutative $C\*$-algebra? Which groups can be obtained as $K$ groups of commutative $C^\*$ algebra (in other words, $K$ groups for topological spaces)?