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2008 Lagrangian matching invariants for fibred four-manifolds: II
Tim Perutz
Geom. Topol. 12(3): 1461-1542 (2008). DOI: 10.2140/gt.2008.12.1461

Abstract

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.

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Tim Perutz. "Lagrangian matching invariants for fibred four-manifolds: II." Geom. Topol. 12 (3) 1461 - 1542, 2008. https://doi.org/10.2140/gt.2008.12.1461

Information

Received: 7 June 2006; Revised: 14 November 2007; Accepted: 11 December 2007; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1144.53104
MathSciNet: MR2421133
Digital Object Identifier: 10.2140/gt.2008.12.1461

Subjects:
Primary: 53D40 , 57R57
Secondary: 57R15

Keywords: Four-manifold , Lagrangian correspondence , Lefschetz fibration , pseudo-holomorphic curve , Seiberg–Witten invariant

Rights: Copyright © 2008 Mathematical Sciences Publishers

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Vol.12 • No. 3 • 2008
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