Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 20, Number 3 (2020), 1073-1126.
Rational homology cobordisms of plumbed manifolds
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.
Algebr. Geom. Topol., Volume 20, Number 3 (2020), 1073-1126.
Received: 24 March 2015
Revised: 30 April 2019
Accepted: 9 September 2019
First available in Project Euclid: 5 June 2020
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Aceto, Paolo. Rational homology cobordisms of plumbed manifolds. Algebr. Geom. Topol. 20 (2020), no. 3, 1073--1126. doi:10.2140/agt.2020.20.1073. https://projecteuclid.org/euclid.agt/1591374776