On the Upsilon invariant and satellite knots

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.

20 pages, 4 figures, to appear in Mathematische Zeitschrift

References in corpus (14)

• Knot Floer homology and the four-ball genus
• Concordance homomorphisms from knot Floer homology
• Knot Floer homology of Whitehead doubles
• Homology Cobordism Invariants and the Cochran-Orr-Teichner Filtration of the Link Concordance Group
• Primary decomposition and the fractal nature of knot concordance
• Bordered Heegaard Floer homology and the tau-invariant of cable knots
• Knot concordance and homology cobordism
• Injectivity of satellite operators in knot concordance
• Knot doubling operators and bordered Heegaard Floer homology
• Corks, exotic 4-manifolds and knot concordance
• Satellite operators with distinct iterates in smooth concordance
• On the Upsilon invariant of cable knots
• The genus filtration in the smooth concordance group
• On the First Singularity for the Upsilon Invariant of Algebraic Knots

Cited by in corpus (7)

• On the Upsilon invariant of cable knots
• Concordance invariants from the $E(-1)$ spectral sequence on Khovanov homology
• Locally equivalent Floer complexes and unoriented link cobordisms
• Rasmussen invariants of Whitehead doubles and other satellites
• On the nonorientable four-ball genus of torus knots
• Linear independence of cables in the knot concordance group
• Twisted Mazur pattern satellite knots and bordered Floer theory