Geodesic
NONSURJECTIVE SATELLITE OPERATORS AND PIECEWISE-LINEAR CONCORDANCE
Forum of Mathematics, Sigma, Tome 4 (2016)

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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. 
@article{10_1017_fms_2016_31,
     author = {ADAM SIMON LEVINE},
     title = {NONSURJECTIVE {SATELLITE} {OPERATORS} {AND} {PIECEWISE-LINEAR} {CONCORDANCE}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {4},
     year = {2016},
     doi = {10.1017/fms.2016.31},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2016.31/}
}
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ADAM SIMON LEVINE. NONSURJECTIVE SATELLITE OPERATORS AND PIECEWISE-LINEAR CONCORDANCE. Forum of Mathematics, Sigma, Tome 4 (2016). doi: 10.1017/fms.2016.31

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