Paul MelvinHom, Jennifer2023-05-222011-04-202011-05-162011-04-20https://repository.upenn.edu/handle/20.500.14332/30297A natural question in knot theory is to ask how certain properties of a knot behave under satellite operations. We will focus on the satellite operation of cabling, and on Heegaard Floer-theoretic properties. In particular, we will give a formula for the Ozsvath-Szabo concordance invariant tau of iterated cables of a knot K in terms of the cabling parameters, tau(K), and a new concordance invariant, epsilon(K). We show that, in many cases, varepsilon gives better bounds on the 4-ball genus of a knot that tau alone, and discuss further applications of epsilon. We will also completely classify when the iterated cable of a knot admits a positive L-space surgery.Heegaard Floerknot Floer homologyconcordancecablesL-spaceGeometry and TopologyMathematicsDissertation/Thesis