Volume 2 (1999)

Download this article
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
MSP Books and Monographs
About this Series
Editorial Board
Ethics Statement
Author Index
Submission Guidelines
Author Copyright Form
Purchases
ISSN (electronic): 1464-8997
ISSN (print): 1464-8989
Other MSP Publications

Topological Field Theories and formulae of Casson and Meng–Taubes

Simon K Donaldson

Geometry & Topology Monographs 2 (1999) 87–102

DOI: 10.2140/gtm.1999.2.87

arXiv: math.GT/9911248

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 S2×S1.

Keywords

Seiberg–Witten invariant, Casson invariant, Alexander polynomial, Milnor torsion, topological quantum field theory, moduli space, vortex equation

Mathematical Subject Classification

Primary: 57R57

Secondary: 57M25, 57N10, 58D29

References
Publication

Received: 5 March 1999
Revised: 24 June 1999
Published: 21 October 1999

Authors
Simon K Donaldson
Department of Mathematics
Imperial College
London
SW7 2BZ
United Kingdom