Grafting Seiberg-Witten monopoles

Details Grafting Seiberg-Witten monopoles Grafting Seiberg-Witten monopoles

2001-10-26

arxiv.org/abs/math/0110285v2

Algebr. Geom. Topol. 3 (2003) 155-185

Mathematics

Symplectic Geometry

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-7.abs.html

Scientific paper

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).

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