Heegaard Floer Invariants and Cabling

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.

Author dc:creator

• Hom, Jennifer

Advisor dc:contributor.advisor

• Paul Melvin

Repository record dc:identifier.uri

https://repository.upenn.edu/handle/20.500.14332/30297

OAI identifier oai:identifier

oai:repository.upenn.edu:20.500.14332/30297