Volume 6, issue 4 (2006)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Vortices and a TQFT for Lefschetz fibrations on 4–manifolds

Michael Usher

Algebraic & Geometric Topology 6 (2006) 1677–1743

arXiv: math.SG/0603128

Abstract

Adapting a construction of D Salamon involving the U(1) vortex equations, we explore the properties of a Floer theory for 3–manifolds that fiber over S1 which exhibits several parallels with monopole Floer homology, and in all likelihood coincides with it. The theory fits into a restricted analogue of a TQFT in which the cobordisms are required to be equipped with Lefschetz fibrations, and has connections to the dynamics of surface symplectomorphisms.

Keywords
Lefschetz fibration, Floer homology, symmetric product, TQFT
Mathematical Subject Classification 2000
Primary: 57R57
Secondary: 57R56, 53D40
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Publication
Received: 10 July 2006
Accepted: 29 August 2006
Published: 21 October 2006
Authors
Michael Usher
Department of Mathematics
Princeton Universtity
Fine Hall
Washington Road
Princeton, NJ 08544
USA