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Adiabatic limit in the Seiberg-Witten equations. (English) Zbl 1075.58009

Buchstaber, V. M. (ed.) et al., Geometry, topology, and mathematical physics. Selected papers from S. P. Novikov’s seminar held in Moscow, Russia, 2002–2003. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3613-7/hbk). Translations. Series 2. American Mathematical Society. 212. Advances in the Mathematical Sciences 55, 281-295 (2004).
Author’s summary: We consider the adiabatic (scaling) limit in the Seiberg-Witten equations on symplectic \(4\)-manifolds and show that it can be regarded as complex analogue of the adiabatic limit in the abelian \((2+1)\)-dimensional Higgs model.
For the entire collection see [Zbl 1051.00009].

MSC:

58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals
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