Mathematics – Geometric Topology
Scientific paper
2010-04-14
Mathematics
Geometric Topology
39 pages, 37 figures. Paper split into two volumes (second to be posted separately) in preparation for submission. Some backgr
Scientific paper
Seidel and Smith introduced in arXiv:1002.2648v3 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 indeed 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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