Monopoles and Four-Manifolds

Edward Witten

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arXiv · hep-th/9411102

Monopoles and Four-Manifolds

Edward Witten

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Abstract

Recent developments in the understanding of $N=2$ supersymmetric Yang-Mills theory in four dimensions suggest a new point of view about Donaldson theory of four manifolds: instead of defining four-manifold invariants by counting $SU(2)$ instantons, one can define equivalent four-manifold invariants by counting solutions of a non-linear equation with an abelian gauge group. This is a ``dual'' equation in which the gauge group is the dual of the maximal torus of $SU(2)$. The new viewpoint suggests many new results about the Donaldson invariants.

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Edward Witten. 1994-11-15. Monopoles and Four-Manifolds. https://arxiv.org/abs/hep-th/9411102

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