A spectral sequence for Lagrangian Floer homology

Details A spectral sequence for Lagrangian Floer homology A spectral sequence for Lagrangian Floer homology

2012-01-23

arxiv.org/abs/1201.4663v1

Mathematics

Symplectic Geometry

Scientific paper

Using the work in progress of Wehrheim and Woodward we prove the existence of a spectral sequence converging to the Floer homology of Lagrangians submanifolds under multiple fibred Dehn twists whose $E_1$ term is given by the hypercube of "resolutions" of the fibered Dehn twists involved. As applications we obtain a spectral sequences from Khovanov homology to symplectic Khovanov homology. We also obtain a spectral sequence converging to \HG homology of a 3-manifold, given by a surface homeomorphism, whose $E_1$ term is given by the different ways of resolving the Dehn twists involved in the homeomorphism. This latter sequence generalizes the spectral sequence of branched double covers to general 3-manifolds (i.e. ones which are not branched double covers of links) however its $E_2$ term is not a topological invariant in general.

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