Vortices and a TQFT for Lefschetz fibrations on 4-manifolds

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.

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

References in corpus (6)

• Singular Lefschetz pencils
• Lagrangian matching invariants for fibred four-manifolds: II
• Rounding corners of polygons and the embedded contact homology of T^3
• The periodic Floer homology of a Dehn twist
• Green functions of higher-order differential operators
• The Gromov invariant and the Donaldson-Smith standard surface count

Cited by in corpus (6)

• Lagrangian matching invariants for fibred four-manifolds: II
• Lagrangian matching invariants for fibred four-manifolds: I
• Symplectic Floer homology of area-preserving surface diffeomorphisms
• A tour of bordered Floer theory
• On cobordism maps on periodic Floer homology
• Invariance property of Morse homology on noncompact manifolds