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Rational symplectic field theory over 2 for exact Lagrangian cobordisms

Tobias Ekholm — 2008

Journal of the European Mathematical Society

We construct a version of rational Symplectic Field Theory for pairs ( X , L ) , where X is an exact symplectic manifold, where L X is an exact Lagrangian submanifold with components subdivided into k subsets, and where both X and L have cylindrical ends. The theory associates to ( X , L ) a -graded chain complex of vector spaces over 2 , filtered with k filtration levels. The corresponding k -level spectral sequence is invariant under deformations of ( X , L ) and has the following property: if ( X , L ) is obtained by joining a...

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