Rational homology cobordisms of plumbed manifolds

We investigate rational homology cobordisms of 3-manifolds with nonzero first Betti number. This is motivated by the natural generalization of the slice-ribbon conjecture to multicomponent links In particular we consider the problem of which rational homology S-1 x S-2 's bound rational homology S-1 x D-3 's. We give a simple procedure to construct rational homology cobordisms between plumbed 3-manifolds. We introduce a family of plumbed 3-manifolds with b(1) = 1. By adapting an obstruction based on Donaldson's diagonalization theorem we characterize all manifolds in our family that bound rational homology S-1 x D-3 's. For all these manifolds a rational homology cobordism to S-1 x S-2 can be constructed via our procedure. Our family is large enough to include all Seifert fibered spaces over the 2-sphere with vanishing Euler invariant. In a subsequent paper we describe applications to arborescent link concordance.