Cube of resolutions complexes for Khovanov-Rozansky homology and knot Floer homology

Cube of resolutions complexes for Khovanov-Rozansky homology and knot Floer homology

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Nathan Dowlin, Princeton University
Fine Hall Common Room

This is a joint Geometry/Topology day.   I will compare the oriented cube of resolutions constructions for Khovanov-Rozansky homology and knot Floer homology. Manolescu conjectured that for singular diagrams (or trivalent graphs) the HOMFLY-PT homology and knot Floer homology are isomorphic - I will show that this conjecture is equivalent to a certain spectral sequence collapsing. This will also lead to a recursion formula for the HOMFLY-PT homology of singular diagrams that categorifies Jaeger's composition product formula.