Fukaya Categories and Picard–Lefschetz Theory [electronic resource] / Paul Seidel
Material type:
TextSeries: Zurich Lectures in Advanced Mathematics (ZLAM)Publisher: Zuerich, Switzerland : European Mathematical Society Publishing House, 2008Description: 1 online resource (334 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783037195635Subject(s): Differential & Riemannian geometry | Differential geometry | Associative rings and algebras | Several complex variables and analytic spacesOther classification: 53-xx | 16-xx | 32-xx Online resources: Click here to access online | cover image Summary: The central objects in the book are Lagrangian submanifolds and their invariants, such as Floer homology and its multiplicative structures, which together constitute the Fukaya category. The relevant aspects of pseudo-holomorphic curve theory are covered in some detail, and there is also a self-contained account of the necessary homological algebra. Generally, the emphasis is on simplicity rather than generality. The last part discusses applications to Lefschetz fibrations, and contains many previously unpublished results. The book will be of interest to graduate students and researchers in symplectic geometry and mirror symmetry. Winner 2010 AMS Veblen Prize in Geometry.
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The central objects in the book are Lagrangian submanifolds and their invariants, such as Floer homology and its multiplicative structures, which together constitute the Fukaya category. The relevant aspects of pseudo-holomorphic curve theory are covered in some detail, and there is also a self-contained account of the necessary homological algebra. Generally, the emphasis is on simplicity rather than generality. The last part discusses applications to Lefschetz fibrations, and contains many previously unpublished results. The book will be of interest to graduate students and researchers in symplectic geometry and mirror symmetry. Winner 2010 AMS Veblen Prize in Geometry.
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