Abelian invariants of doubly slice links

Abstract

We provide obstructions to a link in $S^3$ arising as the cross section of any number of unlinked spheres in $S^4$. 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.

29 pages, 5 figures. Changes in v2: improved exposition and added Lemma 5.6 for clarification