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.
"Rational homology cobordisms of plumbed manifolds." Algebr. Geom. Topol. 20 (3) 1073 - 1126, 2020. https://doi.org/10.2140/agt.2020.20.1073