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New York Journal of Mathematics
Volume 29 (2023), 1363-1372

  

Adam Simon Levine

A note on rationally slice knots

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Published: December 27, 2023.
Keywords: Knot concordance, rational homology concordance, amphichiral knots.
Subject [2020]: 57K10, 57K18.

Abstract
Kawauchi proved that every strongly negative amphichiral knot K ⊂ S3 bounds a smoothly embedded disk in some rational homology ball VK, whose construction a priori depends on K. We show that VK is independent of K up to diffeomorphism. Thus, a single 4-manifold, along with connected sums thereof, accounts for all known examples of knots that are rationally slice but not slice.

Acknowledgements

The author was supported by NSF grant DMS-2203860.


Author information

Adam Simon Levine
Department of Mathematics
Duke University
Durham, NC 27708, USA

alevine@math.duke.edu