Obstructions to shake sliceness for links

TL;DR

This paper explores the concept of shake sliceness for links, establishing obstructions and properties related to shake concordance, and demonstrating that shake slice links have certain algebraic and topological features.

Contribution

It introduces new obstructions to a link being shake slice and connects shake concordance with homology cobordism of zero surgery manifolds.

Findings

Arf invariants vanish for shake slice links and components

Shake slice links bound disjoint disks in a homology 4-ball

Each component of a shake slice link is algebraically slice

Abstract

Shake slice generalizes the notion of a slice link, naturally extending the notion of shake slice knots to links. There is also a relative version, shake concordance, that generalizes link concordance. We show that if two links are shake concordant, then their zero surgery manifolds are homology cobordant. Then we give several obstructions to a link being shake slice; for instance, the Arf invariants vanish for both the link and each component. Finally we show that a shake slice link bounds disjoint disks in a homology 4-ball and hence each component is algebraically slice.