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

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.

44 pages, 41 figures. Many corrections have been made and the exposition has been modified in response to the referee's suggestions. This is the version to appear in the Journal of Symplectic Geometry

References in corpus (4)

• On the Khovanov and knot Floer homologies of quasi-alternating links
• A geometric spectral sequence in Khovanov homology
• An invariant of link cobordisms from symplectic Khovanov homology
• The anti-diagonal filtration: reduced theory and applications

Cited by in corpus (1)

• A geometric spectral sequence in Khovanov homology