Volume 6, issue 1 (2002)

Download this article
For printing
Recent Issues

Volume 23
Issue 7, 3233–3749
Issue 6, 2701–3231
Issue 5, 2165–2700
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Torsion, TQFT, and Seiberg–Witten invariants of $3$–manifolds

Thomas E Mark

Geometry & Topology 6 (2002) 27–58

arXiv: math.DG/9912147

Abstract

We prove a conjecture of Hutchings and Lee relating the Seiberg–Witten invariants of a closed 3–manifold X with b1 1 to an invariant that “counts” gradient flow lines—including closed orbits—of a circle-valued Morse function on the manifold. The proof is based on a method described by Donaldson for computing the Seiberg–Witten invariants of 3–manifolds by making use of a “topological quantum field theory,” which makes the calculation completely explicit. We also realize a version of the Seiberg–Witten invariant of X as the intersection number of a pair of totally real submanifolds of a product of vortex moduli spaces on a Riemann surface constructed from geometric data on X. The analogy with recent work of Ozsváth and Szabó suggests a generalization of a conjecture of Salamon, who has proposed a model for the Seiberg–Witten–Floer homology of X in the case that X is a mapping torus.

Keywords
Seiberg–Witten invariant, torsion, topological quantum field theory
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57R56
References
Forward citations
Publication
Received: 16 October 2001
Accepted: 25 January 2002
Published: 29 January 2002
Proposed: Robion Kirby
Seconded: Ronald Stern, Ronald Fintushel
Authors
Thomas E Mark
Department of Mathematics
University of California
Berkeley
California 94720-3840
USA