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Title: Embedding spheres in knot traces
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.  more » « less
Award ID(s):
1902880
PAR ID:
10329614
Author(s) / Creator(s):
; ; ; ; ;
Date Published:
Journal Name:
Compositio Mathematica
Volume:
157
Issue:
10
ISSN:
0010-437X
Page Range / eLocation ID:
2242 to 2279
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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