## Algebraic & Geometric Topology

### Vortices and a TQFT for Lefschetz fibrations on 4–manifolds

Michael Usher

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 6, Number 4 (2006), 1677-1743.

Dates
Accepted: 29 August 2006
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796603

Digital Object Identifier
doi:10.2140/agt.2006.6.1677

Mathematical Reviews number (MathSciNet)
MR2263047

Zentralblatt MATH identifier
1131.57031

#### Citation

Usher, Michael. Vortices and a TQFT for Lefschetz fibrations on 4–manifolds. Algebr. Geom. Topol. 6 (2006), no. 4, 1677--1743. doi:10.2140/agt.2006.6.1677. https://projecteuclid.org/euclid.agt/1513796603

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