2009/07/31 by Paul Seidel, P. Seidel · 47 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Geometry #Homotopy and Cohomology in Algebraic Topology #Mathematics #Mirror symmetry #Nonlinear Waves and Solitons #Pure mathematics #Symmetry (geometry) #math.AG #math.SG
paper · pdf · doi:10.1007/s00220-009-0944-8
published in Communications in Mathematical Physics 297(2), 515-528 (Springer Science+Business Media) · v2: slightly expanded exposition
arxiv created 2009/08/05 · openalex publication_date 2009/10/24 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the suspension operation on Lefschetz fibrations, which takes p(x) to p(x)-y2. This leaves the Fukaya category of the fibration invariant, and changes the category of the fibre (or more precisely, the subcategory consisting of a basis of vanishing cycles) in a specific way. As an application, we prove part of Homological Mirror Symmetry for the total spaces of canonical bundles over toric del Pezzo surfaces.