Topological field theories and formulae of Casson and Meng-Taubes

Details Topological field theories and formulae of Casson and Meng-Taubes Topological field theories and formulae of Casson and Meng-Taubes

1999-11-17

arxiv.org/abs/math/9911248v1

Geom. Topol. Monogr. 2 (1999), 87-102

Mathematics

Geometric Topology

16 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon2/paper4.abs.html

Scientific paper

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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