Link concordance, Homology cobordism, Shake slice, Shake concordance, Arf invariant
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.
Topology and its Applications
Bosman, Anthony, "Obstructions to Shake Sliceness for Links" (2022). Faculty Publications. 4224.
Post-print version retrieved from https://arxiv.org/abs/2107.07099