#### Volume 6, issue 4 (2006)

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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 $U\left(1\right)$ vortex equations, we explore the properties of a Floer theory for 3–manifolds that fiber over ${S}^{1}$ 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