We discuss generalizations of Ozsvath-Szabo's spectral sequence relating Khovanov homology and Heegaard Floer homology, focusing attention on an explicit relationship between natural Z (resp., 1/2 Z) gradings appearing in the two theories. These two gradings have simple representation-theoretic (resp., geometric) interpretations, which we also review.
Grigsby, J. Elisenda and Wehrli, Stephan M., "On Gradings in Khovanov Homology and Sutured Floer Homology" (2010). Mathematics - Faculty Scholarship. 118.
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