On the anti-diagonal filtration for the Heegaard Floer chain complex of a branched double-cover

Eamonn Tweedy

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arXiv · 1004.2476

On the anti-diagonal filtration for the Heegaard Floer chain complex of a branched double-cover

Eamonn Tweedy

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Abstract

Seidel and Smith introduced the graded fixed-point symplectic Khovanov cohomology group Kh_{symp,inv}(K) for a knot K inside S^{3}, as well as a spectral sequence converging to the Heegaard Floer homology-hat group for the connected sum of the double branched cover with a copy of S^{2}xS^{1}. The E^{1}-page of this spectral sequence is isomorphic to a factor of Kh_{symp,inv}(K). Seidel and Smith proved that Kh_{symp,inv} is a knot invariant. We show here that the higher pages of their spectral sequence are knot invariants also.

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Eamonn Tweedy. 2013-08-19. On the anti-diagonal filtration for the Heegaard Floer chain complex of a branched double-cover. https://arxiv.org/abs/1004.2476

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