Non-concordant links with homology cobordant zero framed surgery manifolds

Abstract

We use topological surgery in dimension four to give sufficient conditions for the zero framed surgery manifold of a 3-component link to be homology cobordant to the 3-torus, which arises from zero framed surgery on the Borromean rings, via a topological homology cobordism preserving the homotopy classes of the meridians. This enables us to give new examples of 3-component links with unknotted components and vanishing pairwise linking numbers, such that any two of these links have homology cobordant zero surgeries in the above sense, but the zero surgery manifolds are not homeomorphic. Moreover the links are not concordant to one another, and in fact they can be chosen to be height n but not height n+1 symmetric grope concordant, for each n which is at least three.