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.

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Stanislav Jabuka
Department of Mathematics, Columbia University
2990 Broadway, New York, NY 10027, USA
Email: jabuka@math.columbia.edu

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