On the Upsilon invariant and satellite knots

Feller, Peter; Park, JungHwan; Ray, Arunima

doi:10.1007/s00209-018-2145-7

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On the Upsilon invariant and satellite knots

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Ray, Arunima
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s00209-018-2145-7
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arXiv:1604.04901.pdf
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Citation

Feller, P., Park, J., & Ray, A. (2019). On the Upsilon invariant and satellite knots. Mathematische Zeitschrift, 292(3-4), 1431-1452. doi:10.1007/s00209-018-2145-7.

Cite as: https://hdl.handle.net/21.11116/0000-0004-83B9-7

Abstract

We study the effect of satellite operations on the Upsilon invariant of Ozsvath-Stipsicz-Szabo. We obtain results concerning when a knot and its satellites are independent; for example, we show that the set
$\{D_{2^i,1}\}_{i=1}^\infty$ is a basis for an infinite rank summand of the group of smooth concordance classes of topologically slice knots, for D the positive clasped untwisted Whitehead double of any knot with positive
tau-invariant, e.g. the right-handed trefoil. We also prove that the image of the Mazur satellite operator on the smooth knot concordance group contains an infinite rank subgroup of topologically slice knots.