Non-surjective satellite operators and piecewise-linear concordance

Adam Simon Levine

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arXiv · 1405.1125

Non-surjective satellite operators and piecewise-linear concordance

Adam Simon Levine

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Abstract

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.

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Adam Simon Levine. 2014-05-06. Non-surjective satellite operators and piecewise-linear concordance. https://arxiv.org/abs/1405.1125

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