Timeline for Decorations in Szabo's combinatorial spectral sequence

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May 23, 2013 at 18:46	comment	added	Andy Manion		Right, odd Khovanov homology is just another way of lifting $\mathbb{Z}/2$ Khovanov homology to the integers, but I think from this HF-of-branched-double-cover perspective it's more of a coincidence that when you reduce mod 2 you don't need the crossing orientations to define the Khovanov edge maps. The orientation you mention is the one I was thinking of, and I think it's still necessary to define the maps in the spectral sequence on the chain level (even though the resulting object is independent of them).
May 23, 2013 at 16:16	comment	added	Reza Rezazadegan		Thank you. However the decoration in odd Khovanov homology seems to be to determine the signs and the authors say if one considers $\Z/2$ coefficients one does not need those decorations. Also the link surgeries spectral sequence (as described in Ozsvath and Szabo's branched double cover paper), doesn't seem to depend on the orientation of the link. (Although in Heegaard-Floer theory one assumes the manifold to be oriented and this together with the framing gives an orientation of the link.)
Apr 22, 2013 at 7:53	history	answered	Andy Manion	CC BY-SA 3.0