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Lagrangian matching
invariants for fibred four-manifolds: II
Tim Perutz |
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Geometry & Topology 12 (2008) 1461–1542
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Abstract |
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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. |
Keywords
four-manifold, Lefschetz fibration, Seiberg–Witten
invariant, pseudo-holomorphic curve, Lagrangian
correspondence
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Mathematical Subject Classification 2000
Primary: 53D40, 57R57
Secondary: 57R15
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References |
Publication
Received: 7 June 2006
Revised: 14 November 2007
Accepted: 11 December 2007
Published: 10 June 2008
Proposed: Peter Oszváth
Seconded: Simon Donaldson, Ron Stern
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Authors |
| Tim Perutz | |
| DPMMS Centre for Mathematical Sciences University of Cambridge Wilberforce Road Cambridge CB3 0WB UK |
Department of Mathematics Columbia University 2990 Broadway New York, NY 10027 USA |
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