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

Seidel and Smith introduced the graded fixed-point symplectic Khovanov cohomology group $Kh_{\rm symp,~inv}(K)$ for a knot $K \subset S^{3}$, as well as a spectral sequence converging to the Heegaard Floer homology group $\widehat{HF}(\Sigma (K) \# (S^2 \times S^1))$ with $E^1$-page isomorphic to a factor of $Kh_{\rm symp,~inv}(K)$ [22]. There the authors proved that $Kh_{\rm symp,~inv}$ is a knot invariant. We show here that the higher pages of their spectral sequence are knot invariants also.

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Published 13 May 2014