Algebraic & Geometric Topology

Vortices and a TQFT for Lefschetz fibrations on 4–manifolds

Michael Usher

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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

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

Received: 10 July 2006
Accepted: 29 August 2006
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]
Secondary: 57R56: Topological quantum field theories 53D40: Floer homology and cohomology, symplectic aspects

Lefschetz fibration Floer homology symmetric product TQFT


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.

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