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A surgery for generalized complex structures on 4-manifolds

Gil R. Cavalcanti·Marco Gualtieri
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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.

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BibTeXRIS

Gil R. Cavalcanti, Marco Gualtieri. 2006-02-15. A surgery for generalized complex structures on 4-manifolds. https://doi.org/10.4310/jdg%2F1180135665

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