Geometry and Topology Seminar

In forthcoming work, Ozsvath and Szabo introduce a new method for computing knot Floer homology. Their new theory applies the ideas of bordered Floer homology to the Kauffman-states Heegaard diagram introduced by the same authors in 2002. I will show that a particular version of their bordered algebra decategorifies to V^n, where V is the vector representation of U_q(sl(1|1)), and that their DA bimodule for a braid B decategorifies to the U_q(sl(1|1))-intertwining map from V^n to V^n induced by B. In the first half of the talk, I will review some facts about bordered Floer homology and U_q(sl(1|1))-representations. In the second half, I will discuss the subset of Ozsvath-Szabo's theory needed to compute the decategorification, and I will show in as much detail as possible how the above correspondence is proved.