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Rational homology cobordisms of plumbed ...
Aceto, Paolo...

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Rational homology cobordisms of plumbed 3-manifolds by Aceto, Paolo ( Author )
Lemonjar Open Access
N.A
13-02-2015
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 S1×S2's bound rational homology S1×D3'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 first Betti number equal to 1. By adapting an obstruction based on Donaldson's diagonalization theorem we characterize all manifolds in F that bound rational homology S1×D3's. For all these manifolds a rational homology cobordism to S1×S2 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. In a subsequent paper we describe applications to arborescent link concordance.
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English
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MYR 0.00
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https://arxiv.org/abs/1502.03863
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