Grafting Seiberg–Witten monopoles

We demonstrate that the operation of taking disjoint unions of $J$ –holomorphic curves (and thus obtaining new $J$ –holomorphic curves) has a Seiberg–Witten counterpart. The main theorem asserts that, given two solutions $(A_{i}, ψ_{i})$ , $i = 0, 1$ of the Seiberg–Witten equations for the ${Spin}^{c}$ –structures $W_{E_{i}}^{+} = E_{i} \oplus (E_{i} \otimes K^{- 1})$ (with certain restrictions), there is a solution $(A, ψ)$ of the Seiberg–Witten equations for the ${Spin}^{c}$ –structure $W_{E}$ with $E = E_{0} \otimes E_{1}$ , obtained by “grafting” the two solutions $(A_{i}, ψ_{i})$ .

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Keywords

symplectic 4–manifolds, Seiberg–Witten gauge theory, $J$–holomorphic curves

Mathematical Subject Classification 2000

Primary: 53D99, 57R57

Secondary: 53C27, 58J05

References

Forward citations

Publication

Received: 24 November 2002

Revised: 27 January 2003

Accepted: 13 February 2003

Published: 21 February 2003

Authors

Stanislav Jabuka
Department of Mathematics Columbia University 2990 Broadway New York, NY 10027 USA

Volume 3, issue 1 (2003)

Stanislav Jabuka

Abstract