The anti-diagonal filtration: reduced theory and applications

Details The anti-diagonal filtration: reduced theory and applications The anti-diagonal filtration: reduced theory and applications

2011-09-15

arxiv.org/abs/1109.3425v1

Mathematics

Geometric Topology

25 pages, 35 figures. Part II of a previous article (arXiv:1004.2476v3), split in preparation for submission. Corrected some

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 in S^{3}, as well as a spectral sequence converging to the Heegaard Floer-hat homology group for the connected sum of the double branched cover and a copy of S^{2}xS^{1} (with E_{1}-page isomorphic to a factor of Kh_{symp,inv}(K)). In a previous paper (arXiv:1004.2476v4), we showed that the higher pages of this spectral sequence are knot invariants. Here we discuss a reduced version of the spectral sequence. Under some degeneration conditions, one obtains a new absolute Maslov grading on the Heegaard Floer group. This occurs when K is a two-bridge knot, and we compute the grading in this case.

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