A surgery for generalized complex structures on 4-manifolds
By G. Cavalcanti, M. Gualtieri. 2006
48 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/1360fbffebfa0a84cd7eed3601e2d49b2ef6f4a9
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Maximally homogeneous para-CR manifolds of semisimple type (2006, unknown): “In fact, as shown in [ 5 ], by doing surgery along an embedded torus in a certain symplectic manifold, it can be shown that the four-manifold 3CP2#19CP2 has a generalized complex structure which is complex on”
- Generalized Complex Geometry (2004, methodology): “However we indicate here that the simple example above was used in [8] to produce, via a surgery on a symplectic 4-manifold, an example of a compact, simply-connected generalized complex 4-manifold which admits neither complex nor symplectic structures.”