Vortices and a TQFT for Lefschetz fibrations on 4-manifolds
arXiv:math/0603128 · doi:10.2140/agt.2006.6.1677
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 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.
This is the version published by Algebraic & Geometric Topology on 21 October 2006