Vortices and a TQFT for Lefschetz fibrations on 4–manifolds

Usher, Michael¹

¹Department of Mathematics, Princeton Universtity, Fine Hall, Washington Road, Princeton, NJ 08544, USA

Algebraic and Geometric Topology, Tome 6 (2006) no. 4, pp. 1677-1743

Résumé

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.

Détail

DOI : 10.2140/agt.2006.6.1677

Keywords: Lefschetz fibration, Floer homology, symmetric product, TQFT

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