Constructing Heegaard knot diagrams for (1,1) knots
Philip Ording, Medgar Evers College, CUNY
Abstract: A (1,1) knot is a knot in a 3-manifold M which intersects each
solid torus of a genus one Heegaard splitting for M in a single trivial arc.
This family of knots includes the torus and two-bridge knots, though it has
yet to be completely classified. This talk will discuss the various
presentations through which (1,1) knots have been studied so far, with an
emphasis on Heegaard knot diagrams. Such diagrams constitute the basic data
for calculating the knot Floer homology invariants, and an algorithm which
constructs a Heegaard knot diagram from a given (1,1) knot will be
demonstrated.