Abelian invariants of doubly slice links

Abstract

We provide obstructions to a link in S3 arising as the cross section of any number of unlinked spheres in S4. Our obstructions arise from the multivariable signature, the Blanchfield form and generalised Seifert matrices. We also obtain obstructions in the case of surfaces of higher genera, leading to a lower bound on the doubly slice genus of links.