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 \(E_0\otimes E_1\).


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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