Document Type
Article
Publication Date
10-1-2021
Published In
Compositio Mathematica
Abstract
The trace of the n-framed surgery on a knot in S³ 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.
Keywords
shake slice, locally flat embedding, Arf invariant, Tristram–Levine signatures, Alexander polynomial
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Recommended Citation
P. Feller, Allison N. Miller, M. Nagel, P. Orson, M. Powell, and A. Ray.
(2021).
"Embedding Spheres In Knot Traces".
Compositio Mathematica.
Volume 157,
Issue 10.
2242-2279.
DOI: 10.1112/S0010437X21007508
https://works.swarthmore.edu/fac-math-stat/297
Comments
This work is freely available under a Creative Commons license.