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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...

Riemann maps in almost complex manifolds

Bernard Coupet, Hervé Gaussier, Alexandre Sukhov (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We prove the existence of stationary discs in the ball for small almost complex deformations of the standard structure. We define a local analogue of the Riemann map and establish its main properties. These constructions are applied to study the local geometry of almost complex manifolds and their morphisms.

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