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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. |
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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.
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Acknowledgements
The author was supported by NSF grant DMS-2203860.
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Author information
Adam Simon Levine
Department of Mathematics
Duke University
Durham, NC 27708, USA
alevine@math.duke.edu
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