Vortices and a TQFT for Lefschetz fibrations on 4-manifolds

Details Vortices and a TQFT for Lefschetz fibrations on 4-manifolds Vortices and a TQFT for Lefschetz fibrations on 4-manifolds

2006-03-06

arxiv.org/abs/math/0603128v3

Algebr. Geom. Topol. 6 (2006) 1677-1743

Mathematics

Symplectic Geometry

This is the version published by Algebraic & Geometric Topology on 21 October 2006

Scientific paper

10.2140/agt.2006.6.1677

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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