## Grafting Seiberg-Witten monopoles.(English)Zbl 1027.57030

Let $$(M,\omega)$$ be a symplectic 4-manifold and $$E_0$$, $$E_1$$ two complex line bundles over $$M$$. Being given solutions $$(A,\psi_i)$$ of the Seiberg-Witten equations for the $$\text{Spin}^c$$-structures associated to $$E_i$$, this paper produces a solution of the Seiberg-Witten equation for the $$\text{Spin}^c$$-structure associated to the tensor product $$E_0\otimes E_1$$.

### MSC:

 57R57 Applications of global analysis to structures on manifolds 53C27 Spin and Spin$${}^c$$ geometry 53D99 Symplectic geometry, contact geometry 58J05 Elliptic equations on manifolds, general theory 57R17 Symplectic and contact topology in high or arbitrary dimension 57N13 Topology of the Euclidean $$4$$-space, $$4$$-manifolds (MSC2010)
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