Vortices and a TQFT for Lefschetz fibrations on 4–manifolds

Usher, Michael

doi:10.2140/agt.2006.6.1677

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Vortices and a TQFT for Lefschetz fibrations on 4–manifolds

Michael Usher

Algebraic & Geometric Topology 6 (2006) 1677–1743

DOI: 10.2140/agt.2006.6.1677

arXiv: math.SG/0603128

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.

Keywords

Lefschetz fibration, Floer homology, symmetric product, TQFT

Mathematical Subject Classification 2000

Primary: 57R57

Secondary: 57R56, 53D40

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Publication

Received: 10 July 2006

Accepted: 29 August 2006

Published: 21 October 2006

Authors

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

Volume 6, issue 4 (2006)