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Title: Khovanov-Rozansky Complexes in the Knot Floer Cube of Resolutions
Authors: Dowlin, Nathan P.
Advisors: Szabo, Zoltan
Contributors: Mathematics Department
Keywords: homology theory
knot theory
low-dimensional topology
Subjects: Mathematics
Issue Date: 2016
Publisher: Princeton, NJ : Princeton University
Abstract: The (untwisted) oriented cube of resolutions for knot Floer homology assigns a complex C_{F} (S) to a singular resolution S of a knot K. Manolescu conjectured that when S is in braid position, the homology H(C_{F}(S)) is isomorphic to the HOMFLY-PT homology of S. Together with a naturality condition on the induced edge maps, this conjecture would prove the spectral sequence from HOMFLY-PT homology to knot Floer homology. Using a basepoint filtration on C_{F}(S), a recursion formula for HOMFLY-PT homology, and additional sln-like differentials on C_{F}(S), we prove this conjecture. Since the isomorphism is not explicitly defined, the naturality of the induced edge maps remains open.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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