%0 Generic %1 donaldson1999topological %A Donaldson, S. K. %D 1999 %K casson field formulae theories topological %T Topological field theories and formulae of Casson and Meng-Taubes %U http://arxiv.org/abs/math/9911248 %X 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.

@misc{donaldson1999topological, 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.}, added-at = {2013-12-23T04:28:53.000+0100}, author = {Donaldson, S. K.}, biburl = {https://www.bibsonomy.org/bibtex/2cdedb5022b8df952bbfa1c66c45501e5/aeu_research}, description = {Topological field theories and formulae of Casson and Meng-Taubes}, interhash = {d8219c80753be48a2fc096e1dc6e001d}, intrahash = {cdedb5022b8df952bbfa1c66c45501e5}, keywords = {casson field formulae theories topological}, note = {cite arxiv:math/9911248Comment: 16 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon2/paper4.abs.html}, timestamp = {2013-12-23T04:28:53.000+0100}, title = {Topological field theories and formulae of Casson and Meng-Taubes}, url = {http://arxiv.org/abs/math/9911248}, year = 1999 }