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NONSURJECTIVE SATELLITE OPERATORS AND PIECEWISE-LINEAR CONCORDANCE

Part of: Differential topology PL-topology Low-dimensional topology

Published online by Cambridge University Press:  23 December 2016

ADAM SIMON LEVINE
ADAM SIMON LEVINE*
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ 08540, USA; [email protected]

Abstract

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We exhibit a knot $P$ in the solid torus, representing a generator of first homology, such that for any knot $K$ in the 3-sphere, the satellite knot with pattern $P$ and companion $K$ is not smoothly slice in any homology 4-ball. As a consequence, we obtain a knot in a homology 3-sphere that does not bound a piecewise-linear disk in any homology 4-ball.

MSC classification

Primary: 57M27: Invariants of knots and 3-manifolds 57R58: Floer homology 57Q60: Cobordism and concordance
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 4 , 2016 , e34
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author 2016

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