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2020 Rational homology cobordisms of plumbed manifolds
Paolo Aceto
Algebr. Geom. Topol. 20(3): 1073-1126 (2020). DOI: 10.2140/agt.2020.20.1073

Abstract

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 S1×S2’s bound rational homology S1×D3’s. We give a simple procedure to construct rational homology cobordisms between plumbed 3–manifolds. We introduce a family of plumbed 3–manifolds with b1=1. By adapting an obstruction based on Donaldson’s diagonalization theorem we characterize all manifolds in our family that bound rational homology S1×D3’s. For all these manifolds a rational homology cobordism to S1×S2 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.

Citation

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

Information

Received: 24 March 2015; Revised: 30 April 2019; Accepted: 9 September 2019; Published: 2020
First available in Project Euclid: 5 June 2020

zbMATH: 07207571
MathSciNet: MR4105549
Digital Object Identifier: 10.2140/agt.2020.20.1073

Subjects:
Primary: 57M27
Secondary: 57M12, 57M25

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.20 • No. 3 • 2020
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