Volume 12, issue 3 (2008)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Lagrangian matching invariants for fibred four-manifolds: II

Tim Perutz

Geometry & Topology 12 (2008) 1461–1542
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.

Keywords
four-manifold, Lefschetz fibration, Seiberg–Witten invariant, pseudo-holomorphic curve, Lagrangian correspondence
Mathematical Subject Classification 2000
Primary: 53D40, 57R57
Secondary: 57R15
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
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