Geodesic
Grafting Seiberg–Witten monopoles
Jabuka, Stanislav1
1Department of Mathematics, Columbia University, 2990 Broadway, New York, NY 10027, USA
Algebraic and Geometric Topology, Tome 3 (2003) no. 1, pp. 155-185
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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 ⊗ K−1) (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).

DOI : 10.2140/agt.2003.3.155
Keywords: symplectic 4–manifolds, Seiberg–Witten gauge theory, $J$–holomorphic curves

Jabuka, Stanislav  1

1 Department of Mathematics, Columbia University, 2990 Broadway, New York, NY 10027, USA 
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Jabuka, Stanislav. Grafting Seiberg–Witten monopoles. Algebraic and Geometric Topology, Tome 3 (2003) no. 1, pp. 155-185. doi: 10.2140/agt.2003.3.155

[1] S Donaldson, I Smith, Lefschetz pencils and the canonical class for symplectic four-manifolds, Topology 42 (2003) 743

[2] D Mcduff, The local behaviour of holomorphic curves in almost complex 4–manifolds, J. Differential Geom. 34 (1991) 143

[3] J W Morgan, Z Szabó, C H Taubes, A product formula for the Seiberg–Witten invariants and the generalized Thom conjecture, J. Differential Geom. 44 (1996) 706

[4] C H Taubes, $\mathrm{SW}{\Rightarrow}\mathrm{Gr}$: from the Seiberg–Witten equations to pseudo-holomorphic curves, J. Amer. Math. Soc. 9 (1996) 845

[5] C H Taubes, $\mathrm{Gr}{\Rightarrow}\mathrm{SW}$: from pseudo-holomorphic curves to Seiberg–Witten solutions, J. Differential Geom. 51 (1999) 203

[6] C H Taubes, $\mathrm{GR}=\mathrm{SW}$: counting curves and connections, J. Differential Geom. 52 (1999) 453

[7] C H Taubes, Counting pseudo-holomorphic submanifolds in dimension 4, J. Differential Geom. 44 (1996) 818

[8] C H Taubes, The Seiberg–Witten invariants and symplectic forms, Math. Res. Lett. 1 (1994) 809

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