Geometry & Topology
- Geom. Topol.
- Volume 11, Number 2 (2007), 759-828.
Lagrangian matching invariants for fibred four-manifolds: I
In a pair of papers, we construct invariants for smooth four-manifolds equipped with ‘broken fibrations’—the singular Lefschetz fibrations of Auroux, Donaldson and Katzarkov—generalising the Donaldson–Smith invariants for Lefschetz fibrations.
The ‘Lagrangian matching invariants’ are designed to be comparable with the Seiberg–Witten invariants of the underlying four-manifold; formal properties and first computations support the conjecture that equality holds. They fit into a field theory which assigns Floer homology groups to three-manifolds fibred over .
The invariants are derived from moduli spaces of pseudo-holomorphic sections of relative Hilbert schemes of points on the fibres, subject to Lagrangian boundary conditions. Part I—the present paper—is devoted to the symplectic geometry of these Lagrangians.
Geom. Topol., Volume 11, Number 2 (2007), 759-828.
Received: 7 June 2006
Revised: 20 April 2007
Accepted: 27 March 2007
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53D40: Floer homology and cohomology, symplectic aspects 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]
Secondary: 57R15: Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
Perutz, Tim. Lagrangian matching invariants for fibred four-manifolds: I. Geom. Topol. 11 (2007), no. 2, 759--828. doi:10.2140/gt.2007.11.759. https://projecteuclid.org/euclid.gt/1513799861