Existence of Symplectic Surfaces

Details Existence of Symplectic Surfaces Existence of Symplectic Surfaces

2008-12-29

arxiv.org/abs/0812.4929v1

Geometry and Topology of Manifolds, 203-217, Fields Inst. Commun., 47, AMS, 2005

Mathematics

Symplectic Geometry

Scientific paper

In this paper we show that every degree 2 homology class of a 2n-dimensional
symplectic manifold is represented by an immersed symplectic surface if it has
positive symplectic area. Moreover, the symplectic surface can be chosen to be
embedded if 2n is at least 6. We also analyze the additional conditions under
which embedded symplectic representatives exist in dimension 4.

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