We construct a version of rational Symplectic Field Theory for pairs , where is an exact symplectic manifold, where is an exact Lagrangian submanifold with components subdivided into subsets, and where both and have cylindrical ends. The theory associates to a -graded chain complex of vector spaces over , filtered with filtration levels. The corresponding -level spectral sequence is invariant under deformations of and has the following property: if is obtained by joining a negative end of a pair to a positive end of a pair , then there are natural morphisms from the spectral sequences of and of to the spectral sequence of . As an application, we show that if is a Legendrian submanifold of a contact manifold then the spectral sequences associated to , where is the symplectization of and where is the Legendrian submanifold consisting of parallel copies of subdivided into subsets, give Legendrian isotopy invariants of .
Cite this article
Tobias Ekholm, Rational symplectic field theory over ℤ<sub>2</sub> for exact Lagrangian cobordisms. J. Eur. Math. Soc. 10 (2008), no. 3, pp. 641–704DOI 10.4171/JEMS/126