On the Upsilon invariant and satellite knots

Peter Feller; JungHwan Park; Arunima Ray

doi:10.1007/s00209-018-2145-7

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arXiv · 1604.04901

On the Upsilon invariant and satellite knots

Peter Feller·JungHwan Park·Arunima Ray

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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.

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Peter Feller, JungHwan Park, Arunima Ray. 2016-04-17. On the Upsilon invariant and satellite knots. https://doi.org/10.1007/s00209-018-2145-7

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