Embedding spheres in knot traces. (20th October 2021) - Feller, Peter; Miller, Allison N.; Nagel, Matthias; Orson, Patrick; Powell, Mark; Ray, Arunima
Abstract: The trace of the $n$ -framed surgery on a knot in $S^{3}$ is a 4-manifold homotopy equivalent to the 2-sphere. We characterise when a generator of the second homotopy group of such a manifold can be realised by a locally flat embedded $2$ -sphere whose complement has abelian fundamental group. Our characterisation is in terms of classical and computable $3$ -dimensional knot invariants. For each $n$, this provides conditions that imply a knot is topologically $n$ -shake slice, directly analogous to the result of Freedman and Quinn that a knot with trivial Alexander polynomial is topologically slice.