Symplectic surfaces and generic J-holomorphic structures on 4-manifolds

Stanislav Jabuka

Symplectic surfaces and generic J-holomorphic structures on 4-manifolds

Symplectic Geometry 2007-05-23 v2

Authors: Stanislav Jabuka

Abstract

It is a well known fact that every embedded symplectic surface $\Sigma$ in a symplectic 4-manifold $(X^4,\omega)$ can be made $J$ -holomorphic for some almost-complex structure $J$ compatible with $\omega$ . In this paper we investigate when such a $J$ can be chosen from a generic set of almost-complex structures. As an application we give examples of smooth and non-empty Seiberg-Witten and Gromov-Witten moduli spaces whose associated invariants are zero.

Keywords

symplectic geometry smooth 4-manifolds holonomy

Cite

@article{arxiv.math/0207052,
  title  = {Symplectic surfaces and generic J-holomorphic structures on 4-manifolds},
  author = {Stanislav Jabuka},
  journal= {arXiv preprint arXiv:math/0207052},
  year   = {2007}
}

Comments

Minor changes were made upon referee's suggestion. Updated references. To be published in Illinois J. Math

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