We investigate rational homology cobordisms of
–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 bound rational
homology
’s.
We give a simple procedure to construct rational homology cobordisms between plumbed
–manifolds. We introduce a
family of plumbed
–manifolds
with
.
By adapting an obstruction based on Donaldson’s diagonalization theorem
we characterize all manifolds in our family that bound rational homology
’s.
For all these manifolds a rational homology cobordism to
can be
constructed via our procedure. Our family is large enough to include all Seifert fibered spaces
over the
–sphere
with vanishing Euler invariant. In a subsequent paper we describe applications to
arborescent link concordance.
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