Date of Award

Spring 2011

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Mathematics

First Advisor

Paul Melvin

Abstract

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 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.

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