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Title: Applications of Heegaard Floer Homology to Knot Concordance
Authors: Truong, Linh My
Advisors: Ozsvath, Peter
Szabo, Zoltan
Contributors: Mathematics Department
Keywords: heegaard floer homology
knot concordance
knot theory
low dimensional topology
Subjects: Mathematics
Issue Date: 2016
Publisher: Princeton, NJ : Princeton University
Abstract: We consider several applications of Heegaard Floer homology to the study of knot concordance. Using the techniques of bordered Heegaard Floer homology, we compute the concordance invariant $\tau$ for a family of satellite knots that generalizes Whitehead doubles. We also construct an integer lift $\tilde\epsilon$ of the concordance invariant $\epsilon$. We introduce an interpretation of $\tilde\epsilon$ in terms of a filtration on $\cfhat(S^3_N K)$ induced by a family of knots $\mu_n \subset S^3_N K$. Finally, we use truncated Heegaard Floer homology to construct a sequence of concordance invariants $\nu_n$ that generalizes previously known concordance invariants $\nu$, $\nu'$, and $\nu^+$.
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Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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