Holomorphic jets in symplectic manifolds

Abstract

We define pointwise partial differential relations for holomorphic discs. Given a relative homotopy class, a relation, and a generic almost complex structure we provide the moduli space of discs which have an injective point with the structure of a smooth manifold. Applications to the local behaviour are given and an adjunction inequality for singularities is derived. Moreover, we show that for a coordinate class of a monotone Lagrangian split torus generically the number of non-immersed holomorphic discs is even.

Improved exposition and stronger results due to referees remarks, appendix added, to appear in J. Fixed Point Theory Appl

References in corpus (2)

• Eliashberg's proof of Cerf's theorem
• The annulus property of simple holomorphic discs

Cited by in corpus (1)

• Diffeomorphism type of symplectic fillings of unit cotangent bundles