Geometry and Topology Seminar

For oriented links in the three sphere, there are two geometric questions: determining Thurston polytopes of the link complements and 4-genera of links with vanishing pairwise linking numbers. I will explain how to use the Heegaard Floer homology introduced by Ozsvath and Szabo to determine the Thurston polytope, and give some bounds on the 4-genus in terms of the so-called d-invariants. In particular, for 2-component L-space links, d-invariants of integral surgeries along the link can be computed, generalizing Ni-Wu's formula for knot surgeries, and Thurston polytopes for such links are determined by Alexander polynomials explicitly. I will also show some examples for both questions.