Geometry & Topology

Lagrangian matching invariants for fibred four-manifolds: II

Tim Perutz

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In the second of a pair of papers, we complete our geometric construction of “Lagrangian matching invariants” for smooth four-manifolds equipped with broken fibrations. We prove an index formula, a vanishing theorem for connected sums and an analogue of the Meng–Taubes formula. These results lend support to the conjecture that the invariants coincide with Seiberg–Witten invariants of the underlying four-manifold, and are in particular independent of the broken fibration.

Article information

Geom. Topol., Volume 12, Number 3 (2008), 1461-1542.

Received: 7 June 2006
Revised: 14 November 2007
Accepted: 11 December 2007
First available in Project Euclid: 20 December 2017

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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.)

four-manifold Lefschetz fibration Seiberg–Witten invariant pseudo-holomorphic curve Lagrangian correspondence


Perutz, Tim. Lagrangian matching invariants for fibred four-manifolds: II. Geom. Topol. 12 (2008), no. 3, 1461--1542. doi:10.2140/gt.2008.12.1461.

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