Heegaard Floer Invariants and Cabling

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Doctor of Philosophy (PhD)
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Mathematics
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Heegaard Floer
knot Floer homology
concordance
cables
L-space
Geometry and Topology
Mathematics
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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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Paul Melvin
Date of degree
2011-05-16
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