A surgery for generalized complex structures on 4-manifolds

Details A surgery for generalized complex structures on 4-manifolds A surgery for generalized complex structures on 4-manifolds

2006-02-15

arxiv.org/abs/math/0602333v1

J. Differential Geom., 76, 35 -- 43, 2007.

Mathematics

Differential Geometry

7 pages

Scientific paper

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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