LAUSR

We study the effect of satellite operations on the Upsilon invariant of Ozsváth–Stipsicz–Szabó. We obtain results concerning when a knot and its satellites are independent; for example, we show that the set $$\{D_{2^i,1}\}_{i=1}^\infty $${D2i,1}i=1∞ 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 $$\tau $$τ-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.