#### Algebraic and Geometric Topology 3 (2003),
paper no. 7, pages 155-185.

## Grafting Seiberg-Witten monopoles

### Stanislav Jabuka

**Abstract**.
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, psi _i), i=0,1 of the Seiberg-Witten equations for the
Spin^c-structure W^+_{E_i}= E_i direct sum (E_i tensor K^{-1}) (with
certain restrictions), there is a solution (A, psi) of the
Seiberg-Witten equations for the Spin^c-structure W_E with E= E_0
tensor E_1, obtained by `grafting' the two solutions (A_i, psi_i).
**Keywords**.
Symplectic 4-manifolds, Seiberg-Witten gauge theory, J-holomorphic curves

**AMS subject classification**.
Primary: 53D99, 57R57.
Secondary: 53C27, 58J05.

**DOI:** 10.2140/agt.2003.3.155

**E-print:** `arXiv:math.SG/0110285`

Submitted: 24 November 2002.
(Revised: 27 January 2003.)
Accepted: 13 February 2003.
Published: 21 February 2003.

Notes on file formats
Stanislav Jabuka

Department of Mathematics, Columbia University

2990 Broadway, New York, NY 10027, USA

Email: jabuka@math.columbia.edu

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