English

A surgery for generalized complex structures on 4-manifolds

Differential Geometry 2023-05-26 v1 Symplectic Geometry

Abstract

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 3 CP^2 # 19 \overline{CP^2}, which has vanishing Seiberg-Witten invariants and hence does not admit complex or symplectic structure.

Keywords

Cite

@article{arxiv.math/0602333,
  title  = {A surgery for generalized complex structures on 4-manifolds},
  author = {Gil R. Cavalcanti and Marco Gualtieri},
  journal= {arXiv preprint arXiv:math/0602333},
  year   = {2023}
}

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7 pages