Lagrangian matching invariants for fibred four-manifolds: II

Perutz, Tim¹

¹ 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

Geometry & topology, Tome 12 (2008) no. 3, pp. 1461-1542.

Résumé

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.

Détail

DOI : 10.2140/gt.2008.12.1461

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

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