Heegaard Floer Invariants and Cabling

HEEGAARD FLOER INVARIANTS AND CABLING Jennifer Hom Paul Melvin, Advisor A 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 Floertheoretic properties. In particular, we will give a formula for the Ozsváth-Szabó concordance invariant τ of iterated cables of a knot K in terms of the cabling parameters, τ(K), and a new concordance invariant, ε(K). We show that, in many cases, ε gives better bounds on the 4-ball genus of a knot that τ alone, and discuss further applications of ε. We will also completely classify when the iterated cable of a knot admits a positive L-space surgery.