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Title: Knot concordance and matrix factorizations
Authors: Ballinger, William
Advisors: Szabo, Zoltan
Contributors: Mathematics Department
Subjects: Mathematics
Issue Date: 2023
Publisher: Princeton, NJ : Princeton University
Abstract: In this thesis, I prove that for the $E(-1)$ spectral sequence constructed by Rasmussen, beginning at the Khovanov-Rozansky $\mathfrak{sl}(n)$ homology of a knot and converging to the homology of the unknot, all higher pages are knot invariants. This is then used to construct a number of numerical knot invariants, each of which is a concordance homomorphism, and these new invariants are applied to obstruct nonorientable surfaces or surfaces in connected sums of $\mathbb{C} P^2$ from bounding a knot, as well as to bounds on the smooth slice genus.
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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