15 apr 2015 -- 14:30
Sala Seminari, DM, Pisa
Seminari di Geometria, Pisa
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 b1=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.