We study the behavior of the Ozsváth–Szabó and Rasmussen knot concordance invariants and on , the –cable of a knot where and are relatively prime. We show that for every knot and for any fixed positive integer , both of the invariants evaluated on differ from their value on the torus knot by fixed constants for all but finitely many . Combining this result together with Hedden’s extensive work on the behavior of on –cables yields bounds on the value of on any –cable of . In addition, several of Hedden’s obstructions for cables bounding complex curves are extended.
"Ozsváth–Szabó and Rasmussen invariants of cable knots." Algebr. Geom. Topol. 10 (2) 825 - 836, 2010. https://doi.org/10.2140/agt.2010.10.825