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Title: Geometry of (1,1)-Knots and Knot Floer Homology
Authors: Racz, Bela Andras
Advisors: Szabo, Zoltan
Contributors: Mathematics Department
Keywords: (1,1)-knots
grid diagrams
Heegaard Floer homology
knot invariants
Subjects: Mathematics
Issue Date: 2015
Publisher: Princeton, NJ : Princeton University
Abstract: We apply the technique of Heegaard Floer Homology to (1,1)-knots (1-bridge knots on the torus) to determine all (1,1)-knots of crossing number up to 12. We also prove miscellaneous results regarding (1,1)-knots, including the existence of a family with trivial Alexander polynomial, and symmetry results. In addition, we define and study a new class of multi-pointed Heegaard diagrams for links in S^3 that generalizes the classical notion of grid diagrams.
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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