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

2010/04/14 by Eamonn Tweedy, Tweedy, Eamonn · 1 citation
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1004.2476

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

arxiv created 2013/08/19 · arxiv updated 2013/08/20

Abstract

Seidel and Smith introduced the graded fixed-point symplectic Khovanov cohomology group Kh_symp,inv(K) for a knot K inside S³, 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 S²xS¹. The E¹-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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• The anti-diagonal filtration: reduced theory and applications

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