Topological field theories and formulae of Casson and Meng-Taubes
Geometric Topology
2016-09-07 v1 Differential Geometry
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.
Keywords
Cite
@article{arxiv.math/9911248,
title = {Topological field theories and formulae of Casson and Meng-Taubes},
author = {S. K. Donaldson},
journal= {arXiv preprint arXiv:math/9911248},
year = {2016}
}
Comments
16 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon2/paper4.abs.html