Rational homology cobordisms of plumbed manifolds and arborescent link concordance
SPEAKER | Paolo Aceto
DATE | May 10(Wed), 2017
TIME | 14:30
PLACE | 8101
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^1xS^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.