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Vortices and a TQFT for Lefschetz fibrations on 4-manifolds

Michael Usher
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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.

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Michael Usher. 2009-05-11. Vortices and a TQFT for Lefschetz fibrations on 4-manifolds. https://doi.org/10.2140/agt.2006.6.1677

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