Volume 8, issue 3 (2004)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21
Issue 6, 3191–3810
Issue 5, 2557–3190
Issue 4, 1931–2555
Issue 3, 1285–1930
Issue 2, 647–1283
Issue 1, 1–645

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A field theory for symplectic fibrations over surfaces

François Lalonde

Geometry & Topology 8 (2004) 1189–1226

arXiv: math.SG/0309335

Abstract

We introduce in this paper a field theory on symplectic manifolds that are fibered over a real surface with interior marked points and cylindrical ends. We assign to each such object a morphism between certain tensor products of quantum and Floer homologies that are canonically attached to the fibration. We prove a composition theorem in the spirit of QFT, and show that this field theory applies naturally to the problem of minimising geodesics in Hofer’s geometry. This work can be considered as a natural framework that incorporates both the Piunikhin–Salamon–Schwarz morphisms and the Seidel isomorphism.

Keywords
symplectic fibration, field theory, quantum cohomology, Floer homology, Hofer's geometry, commutator length
Mathematical Subject Classification 2000
Primary: 53D45
Secondary: 53D40, 81T40, 37J50
References
Forward citations
Publication
Received: 20 September 2003
Revised: 22 August 2004
Accepted: 11 July 2004
Published: 10 September 2004
Proposed: Leonid Polterovich
Seconded: Yasha Eliashberg, Robion Kirby
Authors
François Lalonde
Department of Mathematics and Statistics
University of Montreal
Montreal H3C 3J7
Quebec
Canada