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Grafting Seiberg–Witten monopoles

Stanislav Jabuka

Algebraic & Geometric Topology 3 (2003) 155–185

arXiv: math.SG/0110285

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 (Ai,ψi), i = 0,1 of the Seiberg–Witten equations for the Spinc–structures WEi+ = Ei (Ei K1) (with certain restrictions), there is a solution (A,ψ) of the Seiberg–Witten equations for the Spinc–structure WE with E = E0 E1, obtained by “grafting” the two solutions (Ai,ψi).

Keywords
symplectic 4–manifolds, Seiberg–Witten gauge theory, $J$–holomorphic curves
Mathematical Subject Classification 2000
Primary: 53D99, 57R57
Secondary: 53C27, 58J05
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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