Szabo, ZoltanRacz, Bela AndrasMathematics Department2015-02-082026-09-302015-02-082026-09-302015http://arks.princeton.edu/ark:/88435/dsp01ft848s85jhttps://theses-dissertations.princeton.edu/handle/88435/dsp01ft848s85jWe 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.en(1,1)-knotsgrid diagramsHeegaard Floer homologyknot invariantsMathematicsAcademic dissertations (Ph.D.)