On knot Floer homology of satellite (1,1) knots

A (1,1) knot is a knot K ⊂ S 3 which intersects each solid torus Hi, i = 1, 2, of a genus one Heegaard splitting S3 = H1 ∪ H2 in a single trivial arc. Goda, Matsuda and Morifuji recognized that K is a (1,1) knot if and only if it admits a doubly pointed Heegaard diagram of genus one, as defined by Ozsvath and Szabo. In this case, Ozsvath and Szabo have shown that the knot Floer homology of K is accessible by a combinatorial algorithm. This thesis presents a complementary algorithm for producing a doubly pointed Heegaard diagram from a given (1,1) knot and then applies it in the study of knot Floer homology of certain satellite knots with trefoil companion. The Heegaard diagram algorithm here depends on a parameterization of (1,1) knots by Choi and Ko. The subsequent investigation of satellite knots depends on the classification of satellite (1,1) knots by Morimoto and Sakuma, and a computer program written by Gabriel Doyle is instrumental in the calculations of knot Floer homology herein. There are two appendices: one to implement the Heegaard knot diagram algorithm using Mathematica, and one to catalogue the knot Floer homology data obtained.