Stability and Existence of Surfaces in Symplectic 4-Manifolds with $b^+=1$

Josef G. Dorfmeister; Tian-Jun Li; Weiwei Wu

Stability and Existence of Surfaces in Symplectic 4-Manifolds with $b^+=1$

Symplectic Geometry 2014-07-07 v1 Differential Geometry

Authors: Josef G. Dorfmeister , Tian-Jun Li , Weiwei Wu

Abstract

We establish various stability results for symplectic surfaces in symplectic $4-$ manifolds with $b^+=1$ . These results are then applied to prove the existence of representatives of Lagrangian ADE-configurations as well as to classify negative symplectic spheres in symplectic $4-$ manifolds with $\kappa=-\infty$ . This involves the explicit construction of spheres in rational manifolds via a new construction technique called the tilted transport.

Keywords

symplectic 4-manifolds symplectic surfaces stability lagrangian ade-configurations negative symplectic spheres rational manifolds tilted transport

Cite

@article{arxiv.1407.1089,
  title  = {Stability and Existence of Surfaces in Symplectic 4-Manifolds with $b^+=1$},
  author = {Josef G. Dorfmeister and Tian-Jun Li and Weiwei Wu},
  journal= {arXiv preprint arXiv:1407.1089},
  year   = {2014}
}

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Stability and Existence of Surfaces in Symplectic 4-Manifolds with $b^+=1$

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