Embedding spheres in knot traces

Feller, P., Miller, A. N., Nagel, M., Orson, P., Powell, M. and Ray, A. (2021) Embedding spheres in knot traces. Compositio Mathematica, 157(10), pp. 2242-2279. (doi: 10.1112/s0010437x21007508)

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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.

Item Type:Articles
Additional Information:ANM is supported by NSF DMS-1902880. PF and MN gratefully acknowledge support by the SNSF Grant 181199.
Glasgow Author(s) Enlighten ID:Powell, Dr Mark
Authors: Feller, P., Miller, A. N., Nagel, M., Orson, P., Powell, M., and Ray, A.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Compositio Mathematica
Publisher:Cambridge University Press
ISSN (Online):1570-5846
Published Online:20 October 2021
Copyright Holders:Copyright © 2021 The Author(s)
First Published:First published in Compositio Mathematica 157(10): 2242-2279
Publisher Policy:Reproduced under a Creative Commons license

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