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A surgery for generalized complex structures on 4-manifolds

Gil R. Cavalcanti Mathematical Institute Marco Gualtieri Massachusetts Institute of Technology

Differential Geometry mathscidoc:1609.10016

Journal of Differential Geometry, 76, (1), 35-43, 2007
We introduce a surgery for generalized complex manifolds whose input is a symplectic 4-manifold containing a symplectic 2-torus with trivial normal bundle and whose output is a 4-manifold endowed with a generalized complex structure exhibiting type change along a 2-torus. Performing this surgery on a K3 surface, we obtain a generalized complex structure on 3CP2#19CP2, which has vanishing Seiberg–Witten invariants and hence does not admit complex or symplectic structures.
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@inproceedings{gil2007a,
  title={A SURGERY FOR GENERALIZED COMPLEX STRUCTURES ON 4-MANIFOLDS},
  author={Gil R. Cavalcanti, and Marco Gualtieri},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160908194933367226673},
  booktitle={Journal of Differential Geometry},
  volume={76},
  number={1},
  pages={35-43},
  year={2007},
}
Gil R. Cavalcanti, and Marco Gualtieri. A SURGERY FOR GENERALIZED COMPLEX STRUCTURES ON 4-MANIFOLDS. 2007. Vol. 76. In Journal of Differential Geometry. pp.35-43. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160908194933367226673.
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