Existence of Symplectic Surfaces

2008/12/29 by Tian-Jun Li · 1 citation
Mathematics · #math.SG #math.AG #math.GT

paper · pdf

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

arxiv created 2008/12/29 · arxiv updated 2009/12/01

Abstract

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.

Cited by

• Symplectically aspherical Kähler manifolds, scalar curvature, and the fundamental group

Related

• Symplectic surfaces in a fixed homology class
• Symplectic genus, minimal genus and diffeomorphisms
• Symplectic Classes on Elliptic Surfaces with positive Euler Number
• Extension of 2-forms and symplectic varieties
• Symplectic forms on the space of embedded symplectic surfaces and their reductions