Mathematics Colloquia and Seminars

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For links in the three sphere, there are two geometric questions: determining the Thurston polytope and 4-genus 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 h-function. In particular, for L-space links, the h-function can be computed explicitly by Alexander polynomials of the links and sublinks, and for L-space links with two components, the Thurston polytope is determined by the Alexander polynomials in a combinatorial way. I will also show some examples for both of the questions.