# Rational homology cobordisms of plumbed 3-manifolds and arborescent link concordance

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Paolo Aceto

created by daniele on 13 Apr 2015

15 apr 2015
-- 14:30

Sala Seminari, DM, Pisa

Seminari di Geometria, Pisa

**Abstract.**

We investigate rational homology cobordisms of $3$-manifolds with
non-zero 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 $S^1x
S^2$'s bound rational homology $S^1xD^3$'s. We give a simple procedure to
construct rational homology cobordisms between plumbed 3-manifold. We
introduce a family F of plumbed 3-manifolds with b_{1=1.} By adapting an
obstruction based on Donaldson's diagonalization theorem we
characterize all manifolds in F that bound rational homology
$S^1xD^3$'s. For all these manifolds a rational homology cobordism to
$S^1xS^2$ can be constructed via our procedure.
The family F is large enough to include all Seifert fibered spaces
over the $2$-sphere with vanishing Euler invariant.

We also describe applications to arborescent link concordance.