Lagrangian matching invariants for fibred four-manifolds: II

2006/06/30 by Tim Perutz · 4 citations
Mathematics · #Advanced Combinatorial Mathematics #Computer science #Fibered knot #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Index (typography) #Lagrangian #Matching (statistics) #Mathematics #Pure mathematics #math.GT #math.SG #msc:53D40 #msc:57R15 #msc:57R57

paper · pdf · doi:10.2140/gt.2008.12.1461

published as Geom. Topol. 12 (2008) 1461-1542 · 83 pages, 1 figure - v2 has a new introduction and numerous corrections, most notably concerning orientations and compactness in presence of disconnected fibres

arxiv created 2007/12/19 · openalex publication_date 2008/06/10 · arxiv updated 2014/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 fourmanifold, and are in particular independent of the broken fibration.

Citations

• Floer homology and Novikov rings
• Holomorphic disks and topological invariants for closed three-manifolds
• Introduction to Symplectic Field Theory
• The Stable Homotopy of the Classical Groups
• Lagrangian matching invariants for fibred four-manifolds: I

Cited by

• Symplectic Floer homology of area-preserving surface diffeomorphisms
• Constructing Lefschetz-type fibrations on four-manifolds
• Fiber-connected, indefinite Morse 2-functions on connected n -manifolds
• Elimination of cusps in dimension 4 and its applications