Link invariants related to knot Floer homology and Khovanov homology

Link invariants related to knot Floer homology and Khovanov homology

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Nathan Dowlin, Columbia University
Fine Hall 314

Despite the differences in their constructions, knot Floer homology and Khovanov-Rozansky homology seem to have a great deal in common. I will introduce a family of invariants HFK_n on the knot Floer side which are the knot Floer analogs of sl_n homology. These invariants don't readily allow a cube of resolutions construction, but in the n=2 case I will give an algebraically constructed complex which is expected to be quasi-isomorphic to HFK_2. This complex does decompose as an oriented cube of resolutions, and we will show that the E_2 page of the associated spectral sequence is isomorphic to Khovanov homology. Since reduced HFK_2 is isomorphic to delta-graded HFK, this gives a possible construction of the spectral sequence from Khovanov homology to knot Floer homology. Joint with Akram Alishahi.