Embedding spheres in knot traces
Geometric Topology
2023-04-12 v2
Abstract
The trace of -framed surgery on a knot in 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 , this provides conditions that imply a knot is topologically -shake slice, directly analogous to the result of Freedman and Quinn that a knot with trivial Alexander polynomial is topologically slice.
Keywords
Cite
@article{arxiv.2004.04204,
title = {Embedding spheres in knot traces},
author = {Peter Feller and Allison N. Miller and Matthias Nagel and Patrick Orson and Mark Powell and Arunima Ray},
journal= {arXiv preprint arXiv:2004.04204},
year = {2023}
}
Comments
37 pages, 2 figures. v2 some typos fixed