English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Embedding spheres in knot traces

MPS-Authors
/persons/resource/persons235234

Feller,  Peter
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons267359

Miller,  Allison N.
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons267362

Nagel,  Matthias
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons267365

Orson,  Patrick
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons236018

Powell,  Mark
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons236053

Ray,  Arunima
Max Planck Institute for Mathematics, Max Planck Society;

External Resource
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)
Supplementary Material (public)
There is no public supplementary material available
Citation

Feller, P., Miller, A. N., Nagel, M., Orson, P., Powell, M., & Ray, A. (2021). Embedding spheres in knot traces. Compositio Mathematica, 157(10), 2242-2279. doi:10.1112/S0010437X21007508.


Cite as: https://hdl.handle.net/21.11116/0000-0009-7CA2-5
Abstract
The trace of $n$-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.