Gluing Seiberg-Witten monopoles

We establish a canonical gluing procedure for Seiberg-Witten monopoles on the two pieces of a closed, oriented four-manifold $X$ which is split along a $3$-dimensional closed, oriented submanifold. We only assume that the (unperturbed) character variety is Kuranishi-smooth and the limiting maps are transversal-then we will be able to glue regular monopoles over the irreducible points of the character variety.

2010 Mathematics Subject Classification

Primary 53C07. Secondary 57Rxx, 58Jxx.

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Published 1 January 2005