Topological field theories and formulae of Casson and Meng-Taubes

S. K. Donaldson

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arXiv · math/9911248

Topological field theories and formulae of Casson and Meng-Taubes

S. K. Donaldson

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Abstract

The goal of this paper is to give a new proof of a theorem of Meng and Taubes that identifies the Seiberg-Witten invariants of 3-manifolds with Milnor torsion. The point of view here will be that of topological quantum field theory. In particular, we relate the Seiberg-Witten equations on a 3-manifold with the Abelian vortex equations on a Riemann surface. These techniques also give a new proof of the surgery formula for the Casson invariant, interpreted as an invariant of a homology S^2 x S^1.

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S. K. Donaldson. 1999-11-17. Topological field theories and formulae of Casson and Meng-Taubes. https://arxiv.org/abs/math/9911248

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