NONCONCORDANT LINKS WITH HOMOLOGY COBORDANT ZERO-FRAMED SURGERY MANIFOLDS

Abstract

We use topological surgery theory to give sufficient conditions for the zero-framed surgery manifold of a 3-component link to be homology cobordant to the zero-framed surgery on the Borromean rings (also known as the 3-torus) via a topological homology cobordism preserving the free homotopy classes of the meridians. This enables us to give 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 h but not height h + 1 symmetric grope concordant, for each h which is at least three.